Supersensitivity measurement method and apparatus for non-hermitian system

Abstract

The present disclosure relates to the technical field of sensor sensitivity measurement, and particularly relates to a supersensitivity measurement method and apparatus for a non-Hermitian system. The method comprises: controlling the sequential application of different displacement loads to boundary nodes in a two-dimensional truss structure platform, so as to excite eigenstates, wherein the two-dimensional truss structure platform is used for simulating a target two-dimensional static non-Hermitian system, and the two-dimensional truss structure platform comprises the boundary nodes, internal nodes and links, with the internal nodes being coupled to the boundary nodes by means of the links; detecting displacement fields of the internal nodes under the different displacement loads; on the basis of the displacement fields of the internal nodes, determining eigenvalues corresponding to different eigenstates; and then determining a quantitative relationship between boundary condition perturbations and an energy spectrum response of the target two-dimensional static non-Hermitian system. By means of the present disclosure, a finite-sized two-dimensional truss structure is used to simulate and measure the response of a non-Hermitian system having arbitrary boundary conditions and arbitrary degrees of freedom, thereby realizing the quantitative characterization of the supersensitivity of the non-Hermitian system.

Description

Method and device for detecting ultra-sensitivity of non-hermitian system

[0001] The present application claims priority from the Chinese patent application No. 202411237068.1 filed on September 4, 2024, and entitled "Method and device for detecting ultra-sensitivity of non-hermitian system", the content of which is incorporated herein by reference in its entirety. TECHNICAL FIELD

[0002] The present disclosure relates to the technical field of sensor sensitivity measurement, and in particular to a method and device for detecting ultra-sensitivity of non-hermitian system. BACKGROUND

[0003] Non-hermitian system corresponds to a class of open physical systems with non-conserved energy, such as damped elastic vibration system, ultra-cold atomic system, heat diffusion system and circuit system, etc. Non-hermitian system exchanges energy with the external environment, and the energy of the system is not closed and conserved, i.e. in the non-hermitian system, energy can flow in or out, resulting in changes in the energy state of the non-hermitian system over time.

[0004] The energy spectrum of the non-hermitian system is extremely sensitive to boundary condition perturbations (such as changes in coupling parameters between boundary nodes), and the sensitivity is positively correlated with the degrees of freedom of the non-hermitian system, which makes the non-hermitian system have broad application prospects in constructing ultra-sensitive sensors. How to detect the energy spectrum response of the non-hermitian system caused by arbitrary boundary condition perturbations under different degrees of freedom has become a key to constructing ultra-sensitive non-hermitian sensors.

[0005] At present, existing non-hermitian systems usually correspond to non-conservative dynamic systems (i.e. dynamic non-hermitian systems), the energy spectrum of the non-hermitian system is extracted by measuring the dynamic response of the non-hermitian system under an external wave signal, and the boundary condition perturbation is applied by adjusting the coupling parameters between the boundary nodes. However, the dynamic non-hermitian system often needs the active driving action of the external environment to break the reciprocity of the system, and at the same time, the boundary condition perturbation cannot be precisely controlled, and the upper limit of the physically allowable degrees of freedom exists. These factors make it impossible to detect the energy spectrum response of the dynamic non-hermitian system caused by arbitrary boundary condition perturbations under arbitrary degrees of freedom, thereby lacking the ability to quantitatively analyze the ultra-sensitivity of the energy spectrum of the non-hermitian system. SUMMARY

[0006] In view of this, the present disclosure provides a method and device for detecting ultra-sensitivity of non-hermitian system, an electronic device and a storage medium.

[0007] According to an aspect of the present disclosure, a method for detecting ultra-sensitivity of non-hermitian system is provided, the method comprising:

[0008] The control applies different displacement loads to boundary nodes in a two-dimensional truss structure platform in turn, the displacement loads are used as boundary condition disturbances for exciting eigenstates of a target two-dimensional static non-Hermitian system, and the eigenstates excited by different displacement loads are different; wherein, the two-dimensional truss structure platform is used for simulating the target two-dimensional static non-Hermitian system, and the two-dimensional truss structure platform comprises a plurality of boundary nodes, a plurality of internal nodes and a plurality of connecting rods; the plurality of boundary nodes are used for simulating boundaries of the target two-dimensional static non-Hermitian system, and the plurality of internal nodes are used for simulating the interior of the target two-dimensional static non-Hermitian system, and any internal node is coupled with at least one boundary node in the plurality of boundary nodes through at least one connecting rod in the plurality of connecting rods;

[0009] Detecting displacement fields of internal nodes in the two-dimensional truss structure platform under the different displacement loads;

[0010] Determining eigenvalues corresponding to different eigenstates based on the displacement fields of the internal nodes in the two-dimensional truss structure platform;

[0011] Determining a quantitative relationship between the boundary condition disturbances and the energy spectrum response of the target two-dimensional static non-Hermitian system based on the different displacement loads and the eigenvalues corresponding to the different eigenstates; wherein, the energy spectrum response comprises a plurality of eigenvalues.

[0012] In a possible implementation, the determining the quantitative relationship between the boundary condition disturbances and the energy spectrum response of the target two-dimensional static non-Hermitian system further comprises:

[0013] Obtaining a quantitative relationship between boundary condition disturbances corresponding to different degrees of freedom of the target two-dimensional static non-Hermitian system and the energy spectrum response of the target two-dimensional static non-Hermitian system in the case that the target two-dimensional static non-Hermitian system has different degrees of freedom;

[0014] Determining a quantitative relationship between degrees of freedom, boundary condition disturbances and the energy spectrum response of the target two-dimensional static non-Hermitian system based on the different degrees of freedom and the quantitative relationship between the boundary condition disturbances corresponding to the different degrees of freedom and the energy spectrum response of the target two-dimensional static non-Hermitian system.

[0015] In a possible implementation, the method further comprises:

[0016] Determining displacement loads to be applied to each boundary node in the two-dimensional truss structure platform for exciting an eigenstate corresponding to the eigenstate ψ of the target two-dimensional static non-Hermitian system based on any eigenstate ψ of the target two-dimensional static non-Hermitian system; wherein, the displacement load to be applied to each boundary node coupled with an internal node is a component of the eigenstate ψ or λ 2 a component of the eigenstate ψ, wherein λ represents an eigenvalue corresponding to the eigenstate ψ.

[0017] In a possible implementation, the plurality of boundary nodes and the plurality of internal nodes are arranged in an M*N manner; M represents a number of nodes arranged in a first direction, and N represents a number of nodes arranged in a second direction, and M and N are both integers greater than 2.

[0018] The determining of the displacement load to be applied to each boundary node in the two-dimensional truss structure platform corresponding to the eigenstate ψ includes:

[0019] For each boundary node at the first boundary, the displacement load to be applied to the boundary node is sequentially the (a-1)th to (M+a-2)th components of the eigenstate ψ, where the value of a is determined by the base structure of the target two-dimensional static non-Hermite system.

[0020] For each boundary node at the second boundary, the displacement load to be applied to the boundary node is sequentially the (a-1)th to (M+a-2)th components of the eigenstate ψ. 2

[0021] The first boundary and the second boundary are two boundaries of the two-dimensional truss structure platform along the first direction.

[0022] In a possible implementation, the determining of the eigenvalue corresponding to different eigenstates based on the displacement field of the internal nodes in the two-dimensional truss structure platform includes:

[0023] For any eigenstate ψ, the real part and the imaginary part of the eigenvalue λ corresponding to the eigenstate ψ are determined based on the displacement field of the internal nodes in the two-dimensional truss structure platform and the eigenstate ψ, to obtain the eigenvalue λ.

[0024] In a possible implementation, the two-dimensional truss structure platform further includes a base and a plurality of slide rods, wherein the plurality of slide rods are arranged along the second direction, and the plurality of boundary nodes and the plurality of internal nodes are connected to the base through the plurality of slide rods, to limit the movement of the plurality of internal nodes and the plurality of boundary nodes in the second direction; and the base is configured to support the plurality of slide rods, the plurality of connecting rods, the plurality of internal nodes, and the plurality of boundary nodes.

[0025] In a possible implementation, the determining of the displacement load to be applied to each boundary node at the first boundary sequentially as the (a-1)th to (M+a-2)th components of the eigenstate ψ includes:

[0026] For each boundary node at the first boundary, the first displacement load to be applied to the boundary node is sequentially the real part of the (a-1)th to (M+a-2)th components of the eigenstate ψ, and the second displacement load to be applied to the boundary node is sequentially the imaginary part of the (a-1)th to (M+a-2)th components of the eigenstate ψ. ​

[0027] for each boundary node at the second boundary, the displacement load to be applied to the boundary node is λ 2 the real parts of the a-1th to M+a-2th components of ψ, the second displacement load to be applied is λ

[0028] for each boundary node at the second boundary, the first displacement load to be applied to the boundary node is λ 2 the real parts of the a-1th to M+a-2th components of ψ, the second displacement load to be applied is λ 2 the imaginary parts of the a-1th to M+a-2th components of ψ;

[0029] the displacement field of the internal nodes in the two-dimensional truss structure platform under the different displacement loads, includes:

[0030] detecting a first displacement field of the internal nodes in the two-dimensional truss structure platform when corresponding first displacement loads are applied to each boundary node at the first boundary and the second boundary;

[0031] detecting a second displacement field of the internal nodes in the two-dimensional truss structure platform when corresponding second displacement loads are applied to each boundary node at the first boundary and the second boundary;

[0032] for any eigenstate ψ, based on the displacement field of the internal nodes in the two-dimensional truss structure platform and the eigenstate ψ, determining the real part and the imaginary part of the eigenvalue λ corresponding to the eigenstate ψ, includes:

[0033] based on the first displacement field, the second displacement field, the first displacement loads applied to each boundary node at the first boundary and the second boundary, and the second displacement loads applied to each boundary node at the first boundary and the second boundary, calculating the real part and the imaginary part of the eigenvalue λ.

[0034] According to another aspect of the present disclosure, a device for detecting non-Hermite system super-sensitivity is provided, the device comprising:

[0035] a displacement load module for controlling different displacement loads to be applied to boundary nodes in a two-dimensional truss structure platform in turn, the displacement loads serving as boundary condition perturbations for exciting eigenstates of a target two-dimensional static non-Hermite system, different eigenstates being excited by different displacement loads; wherein the two-dimensional truss structure platform is used to simulate the target two-dimensional static non-Hermite system, the two-dimensional truss structure platform comprising a plurality of boundary nodes, a plurality of internal nodes and a plurality of connecting rods; the plurality of boundary nodes are used to simulate the boundary of the target two-dimensional static non-Hermite system, the plurality of internal nodes are used to simulate the interior of the target two-dimensional static non-Hermite system, and any internal node is coupled to at least one boundary node in the plurality of boundary nodes through at least one connecting rod in the plurality of connecting rods.

[0036] a detection module configured to detect a displacement field of internal nodes in the two-dimensional truss structure platform under the different displacement loads;

[0037] The detection module is further configured to determine eigenvalues corresponding to different eigenstates based on the displacement field of internal nodes in the two-dimensional truss structure platform.

[0038] An analysis module is configured to determine a quantitative relationship between a boundary condition perturbation and an energy spectrum response of the target two-dimensional static non-Hermitian system based on the different displacement loads and the eigenvalues corresponding to different eigenstates, wherein the energy spectrum response includes a plurality of eigenvalues.

[0039] According to another aspect of the present disclosure, an electronic device is provided, comprising: a processor; a memory for storing processor-executable instructions; wherein the processor is configured to implement the above method when executing the instructions stored in the memory.

[0040] According to another aspect of the present disclosure, a non-volatile computer-readable storage medium having computer program instructions stored thereon is provided, wherein the computer program instructions are executed by a processor to implement the above method.

[0041] According to another aspect of the present disclosure, a computer program product is provided, comprising computer-readable code, or a non-volatile computer-readable storage medium carrying computer-readable code, when the computer-readable code is run in a processor of an electronic device, the processor in the electronic device executes the above method.

[0042] By aspects of the present disclosure, different displacement loads are sequentially applied to boundary nodes in a two-dimensional truss structure platform as boundary condition perturbations for exciting eigenstates of a target two-dimensional static non-Hermitian system, and the eigenstates excited by different displacement loads are different; wherein the two-dimensional truss structure platform is used to simulate the target two-dimensional static non-Hermitian system, and the two-dimensional truss structure platform includes a plurality of boundary nodes, a plurality of internal nodes, and a plurality of connecting rods; the plurality of boundary nodes are used to simulate the boundary of the target two-dimensional static non-Hermitian system, the plurality of internal nodes are used to simulate the interior of the target two-dimensional static non-Hermitian system, and any internal node is coupled with at least one boundary node in the plurality of boundary nodes through at least one connecting rod in the plurality of connecting rods; in this way, a static non-Hermitian system (i.e., a target two-dimensional static non-Hermitian system) with arbitrary boundary condition perturbations and arbitrary degrees of freedom is simulated by using a two-dimensional truss structure platform of a limited size that is constructed in advance, so as to detect the energy spectrum response of an equivalent one-dimensional non-Hermitian system with arbitrary degrees of freedom under the action of boundary condition perturbations; at the same time, since the two-dimensional truss structure platform is formed by pure mechanical elements cooperating with each other, it does not need energy gain and dissipation or active driving action of an external environment, so that a static non-Hermitian system with arbitrary adjustable boundary conditions and arbitrary degrees of freedom and without energy gain or dissipation can be simulated, thereby greatly reducing the complexity of the experiment; and since the two-dimensional truss structure platform belongs to a statics system, it has stronger robustness to perturbations such as damping or structural defects, and the displacement amount of the internal node is macroscopic and has a scale of centimeter level, so that the accuracy and stability of the experimental measurement value are higher. Further, the displacement field of the internal node in the two-dimensional truss structure platform under the different displacement loads is detected; based on the displacement field of the internal node in the two-dimensional truss structure platform, eigenvalues corresponding to different eigenstates are determined; and thus the precise measurement of the eigenenergy spectrum of a non-Hermitian system with arbitrary boundary condition perturbations and arbitrary degrees of freedom is realized. Finally, based on the different displacement loads and the eigenvalues corresponding to different eigenstates, a quantitative relationship between the boundary condition perturbation and the energy spectrum response of the target two-dimensional static non-Hermitian system is determined; as an example, a quantitative relationship between the energy spectrum response of the target two-dimensional static non-Hermitian system and the degrees of freedom and the boundary condition perturbation of the target two-dimensional static non-Hermitian system can be established, thereby providing a basis for quantitatively analyzing the perturbation sensitivity of the energy spectrum of the non-Hermitian system and providing support for designing and manufacturing an ultra-sensitive non-Hermitian sensor.

[0043] Other features and aspects of the present disclosure will become apparent from the following detailed description of example embodiments with reference to the drawings. BRIEF DESCRIPTION OF DRAWINGS

[0044] The accompanying drawings, which are incorporated in and form a part of the specification, illustrate examples of the present disclosure and together with the description, serve to explain the principles of the present disclosure.

[0045] FIG. 1 shows a structural schematic diagram of a non-Hermite system ultra-sensitivity detection system according to an embodiment of the present disclosure;

[0046] FIG. 2 shows a connection geometry schematic diagram of a two-dimensional truss structure platform 20 according to an embodiment of the present disclosure;

[0047] FIG. 3 shows a three-dimensional structure schematic diagram of a two-dimensional truss structure platform 20 according to an embodiment of the present disclosure;

[0048] FIG. 4 shows a three-dimensional structure schematic diagram of a connecting rod according to an embodiment of the present disclosure;

[0049] FIG. 5 shows a three-dimensional structure schematic diagram of an inner sleeve in a connecting rod according to an embodiment of the present disclosure;

[0050] FIG. 6 shows a three-dimensional structure schematic diagram of an outer sleeve in a connecting rod according to an embodiment of the present disclosure;

[0051] FIG. 7 shows a three-dimensional structure schematic diagram of a boundary node according to an embodiment of the present disclosure;

[0052] FIG. 8 shows a three-dimensional structure schematic diagram of an internal node according to an embodiment of the present disclosure;

[0053] FIG. 9 shows a flowchart of a non-Hermite system ultra-sensitivity detection method according to an embodiment of the present disclosure;

[0054] FIG. 10 shows a decay spectrum distribution schematic diagram under a periodic boundary condition according to an embodiment of the present disclosure;

[0055] FIG. 11 shows a detection result of a two-dimensional static non-Hermite system energy spectrum in a scene one, a scene two and a scene three according to an embodiment of the present disclosure;

[0056] FIG. 12 shows a structural schematic diagram of a non-Hermite system ultra-sensitivity detection device according to an embodiment of the present disclosure;

[0057] FIG. 13 is a block diagram of an electronic device 1900 according to an example embodiment. DETAILED DESCRIPTION

[0058] Various exemplary embodiments, features and aspects of the present disclosure will be explained in detail below with reference to the accompanying drawings. The same reference numbers in different drawings denote the same or similar elements. Although various aspects of the embodiments are illustrated in the drawings, the drawings are not necessarily drawn to scale unless specifically noted.

[0059] Reference within the specification to "one embodiment" or "some embodiments" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the disclosure. The appearances of the phrase "in one embodiment" or "in some embodiments" in various places in the specification are not necessarily all referring to the same embodiment, however, are meant to signify that "one or more, but not all embodiments" of the disclosure so described are contemplated to develop a full appreciation of the disclosure. It will be understood that such described features, structures, or characteristics are not to be interpreted as essential features, structures, or characteristics of the embodiments of the disclosure, unless otherwise specifically indicated.

[0060] In the present disclosure, "at least one" means one or more, and "multiple" means two or more. The "and / or" describes the association relationship of the associated objects, which means that there can be three relationships, for example, A and / or B, which can represent the following cases: A exists alone, A and B exist together, and B exists alone, where A and B can be singular or plural. The character " / " generally represents an "or" relationship between the front and rear associated objects. "At least one of the following" or the like means any combination of these items, including any combination of single or multiple items. For example, at least one of a, b, or c can represent a, b, c, a-b, a-c, b-c, or a-b-c, where a, b, and c can be single or multiple.

[0061] In addition, in order to better illustrate the present disclosure, a large number of specific details are given in the specific embodiments below. Those skilled in the art should understand that the present disclosure can also be implemented without some specific details. In some examples, methods, means, elements and circuits that are well known to those skilled in the art are not described in detail, in order to highlight the main idea of the present disclosure.

[0062] The present disclosure provides a kind of super sensitivity detection method of non-Hermite system based on statics (see detailed description in the following text);Different from the non-Hermite system based on wave dynamics, the present disclosure utilizes a finite size two-dimensional truss structure platform, which is a conservative and two-dimensional static non-Hermite system without active driving effect, simulates an equivalent one-dimensional dynamic non-Hermite system with arbitrary boundary conditions and arbitrary degrees of freedom, so as to realize the super sensitivity of the energy spectrum of non-Hermite system under the action of perturbation is measured.

[0063] First, the structure of a non-Hermite system super sensitivity detection system provided by the embodiments of the present disclosure will be exemplarily described.

[0064] FIG. 1 shows a structural schematic diagram of a non-Hermitian system super-sensitivity detection system according to an embodiment of the present disclosure. As shown in FIG. 1, the non-Hermitian system super-sensitivity detection system can include a control device 100 and a two-dimensional truss structure platform 20; wherein the two-dimensional truss structure platform 20 corresponds to a static non-Hermitian system, and the platform can simulate a non-conservative one-dimensional dynamic non-Hermitian system. The control device 100 is configured to perform the non-Hermitian system super-sensitivity detection method provided by the embodiments of the present disclosure. For example, the control device 100 can control the application of boundary condition perturbation to the two-dimensional truss structure platform 20, and detect the energy spectrum response of the two-dimensional truss structure platform 20 (i.e., the two-dimensional static non-Hermitian system), and then determine the quantitative relationship between the boundary condition perturbation and the energy spectrum response of the static non-Hermitian system.

[0065] The two-dimensional truss structure platform 20 includes a plurality of boundary nodes, a plurality of internal nodes, and a plurality of connecting rods. The plurality of boundary nodes are configured to simulate the boundary of the static non-Hermitian system, and the plurality of internal nodes are configured to simulate the interior of the static non-Hermitian system. Any internal node is coupled to at least one boundary node through at least one connecting rod.

[0066] For example, the plurality of boundary nodes and the plurality of internal nodes in the two-dimensional truss structure platform 20 are arranged in M*N. M represents the number of nodes arranged in the first direction, and N represents the number of nodes arranged in the second direction. Both M and N are integers greater than 2, i.e., M and N satisfy the constraints M>2 and N>2. For example, the first direction can be perpendicular to the second direction, e.g., the first direction can be the horizontal direction (denoted as m’ direction), and the second direction can be the vertical direction (denoted as n’ direction). That is, along the horizontal direction, each row is arranged with M nodes, which can be boundary nodes and / or internal nodes; along the vertical direction, each column is arranged with N nodes, which can be boundary nodes and / or internal nodes.

[0067] As an example, the two-dimensional truss structure platform 20 can further include a base and a plurality of slide rods. The plurality of slide rods are arranged along the second direction, and the plurality of boundary nodes and the plurality of internal nodes are connected to the base through the plurality of slide rods to limit the movement of the plurality of internal nodes and the plurality of boundary nodes in the second direction. The base is configured to support the plurality of slide rods, the plurality of connecting rods, the plurality of internal nodes, and the plurality of boundary nodes.

[0068] For example, taking M = 12 and N = 3 as an example, that is, the number of nodes in the horizontal direction of the two-dimensional truss structure platform 20 is M = 12, and the number of nodes in the vertical direction is N = 3. FIG. 2 shows a connection geometry diagram of a two-dimensional truss structure platform 20 according to an embodiment of the present disclosure, and FIG. 3 shows a three-dimensional structure diagram of a two-dimensional truss structure platform 20 according to an embodiment of the present disclosure. As shown in FIGS. 2 and 3, the two-dimensional truss structure platform 20 includes 36 nodes, which can be divided into boundary nodes 4 and internal nodes 5. The boundary nodes 4 can be nodes at the upper boundary, lower boundary, left boundary and right boundary of the two-dimensional truss structure platform 20, as shown by the black dots in FIG. 2, and there are 26 boundary nodes 4 in total. The internal nodes 5 can be other nodes in the two-dimensional truss structure platform 20 except the boundary nodes 4, as shown by the white dots in FIG. 2, and there are 10 internal nodes 5 in total. Two adjacent internal nodes 5 form a unit cell, which can be labeled by a binary array (m, n), where m represents the coordinate value of the unit cell in the vertical direction, and n represents the coordinate value of the unit cell in the horizontal direction. The unit cell refers to the smallest volume unit that can repeat the entire crystal structure through translation operation in a periodic crystal structure. In FIG. 2, each unit cell has two internal nodes 5, and the unit cells are located in the second row (n = 1). Each unit cell is labeled as (1, 1), (2, 1), (3, 1), (4, 1), (5, 1). For any internal node 5, four connecting rods 3 (i.e., single solid line, single dashed line, double solid line and double dashed line in FIG. 2) are coupled to four different boundary nodes 4, respectively. That is, for the boundary nodes 4 adjacent to the internal node 5 in the diagonal direction, the connecting rods 3 are used to couple the two nodes. The stiffness of the four connecting rods 3 is represented by k1-k4, respectively. As shown in FIG. 3, the two-dimensional truss structure platform 20 further includes a base and a plurality of slide rods 2. Each slide rod 2 passes through one boundary node 4, one internal node 5 and another boundary node 4 in the vertical direction (n' direction), and the two ends of the slide rod 2 are fixed on the base, so that the boundary nodes 4 and the internal nodes 5 on the slide rod 2 are limited to move only in the vertical direction. It should be noted that, since in FIG. 2, at n = 1, that is, in the second row in the horizontal direction (m' direction), the left and right boundary nodes 4 and the internal nodes 5 are not coupled (i.e., no connecting rods 3 are connected), therefore, in FIG. 3, the left and right boundary nodes 4 at n = 1 in FIG. 2 are not shown.

[0069] In a possible implementation, as shown in FIG. 3, the base can be a frame composed of a bottom plate 6, wing plates 7, and a loading plate 8, and the frame has a U-shaped cross section; the bottom plate 6 and the wing plates 7 are used to support the two-dimensional truss structure platform 20; the wing plates 7 are placed on the upper and lower sides of the bottom plate 6, and are provided with equidistant through holes in the horizontal direction, and the distance between adjacent through holes is equal to one-half of the crystal constant of the two-dimensional truss structure platform 20 in the horizontal direction, wherein the value of the crystal constant can be set according to requirements. Exemplarily, the bottom plate 6 and the wing plates 7 are both prepared by laser cutting technology, and the material is selected to be acrylic, so as to facilitate processing and manufacturing and save costs. The loading plate 8 is placed in the groove of the bottom plate 6, and is provided with a blind hole, and by matching the bottom protrusion of the boundary node 4 with the blind hole, the displacement load applied to the boundary node 4 in the two-dimensional truss structure platform 20 is realized, and only by adjusting the position of the blind hole on the loading plate 8, the size of the applied displacement load can be changed; exemplarily, the diameter of the blind hole on the loading plate 8 is 11.4-13.4 mm, and is preferably 12.4 mm.

[0070] In a possible implementation, the slide rod 2 in FIG. 3 is made of a rigid material, which is used to limit the displacement mode of the nodes (including the boundary nodes 4 and the internal nodes 5 in FIG. 3) through which the slide rod 2 passes. The slide rod 2 can be an elongated cylindrical structure; exemplarily, the number of the slide rods 2 is M, which are cylindrical metal rods, the slide rod 2 passes through the inside of the through hole of the adjacent nodes arranged in the vertical direction, and the two ends pass through the inside of the through hole of the upper and lower wing plates 7, so as to limit the nodes to only move in the vertical direction. That is, each slide rod 2 passes through the wing plate 7 on the upper side, a boundary node 4 on the upper boundary, an internal node 5, a boundary node 4 on the lower boundary, and the wing plate 7 on the lower side in turn. Exemplarily, the material of the slide rod 2 is stainless steel. Exemplarily, the length of the slide rod 2 is 340-400 mm, and is preferably 370 mm; the diameter of the slide rod 2 is 6-8 mm, and is preferably 7 mm.

[0071] In one possible implementation, the link 3 in FIG. 3 is made of a linear elastic material, and is used to couple the nodes (including one boundary node 4 and one internal node 5 in FIG. 3) connected at both ends of the link 3. As an example, the link 3 is a spring, and a sleeve is provided outside the spring to prevent instability of the spring during compression, and hollow rings are provided at both ends of the sleeve to achieve coupling between the nodes by sleeving the hollow rings on the nodes connected at both ends. FIG. 4 shows a schematic diagram of a perspective structure of a link according to one embodiment of the present disclosure, FIG. 5 shows a schematic diagram of a perspective structure of an inner sleeve of a link according to one embodiment of the present disclosure, and FIG. 6 shows a schematic diagram of a perspective structure of an outer sleeve of a link according to one embodiment of the present disclosure. As shown in FIGS. 3-6, the link 3 is assembled by an inner sleeve 9, an outer sleeve 10, a spring 11, and a fixing sheet 12; wherein the inner sleeve 9 is a cylindrical structure, one end of which is provided with a hollow ring and is sleeved on a ring-shaped support on an outer wall of a node, and the other end of the inner sleeve 9 is provided with a cylindrical protrusion with a slightly smaller diameter; the outer sleeve 10 is provided with a hollow ring at one end and is sleeved on a ring-shaped support on an outer wall of a node, and the other end of the outer sleeve 10 is a thin-walled cylinder with a slit formed above; the spring 11 is adhered at one end to the cylindrical protrusion of the inner sleeve 9 and extends into the thin-walled cylinder of the outer sleeve 10 at the other end; the fixing sheet 12 is a rectangular thin plate structure, which is inserted into the end of the spring 11 by extending into the slit of the outer sleeve 10, so as to fix the end of the spring 11; the spring 11 is a linear spring with equal tensile and compressive stiffness, which provides coupling between the nodes connected at both ends, and the presence of the outer sleeve 10 prevents instability of the spring 11 during compression; for links 3 in different oblique directions, the inner sleeve 9 and the outer sleeve 10 are respectively sleeved on the upper and lower ring-shaped supports on the outer wall of the node to prevent mutual crossing. As an example, the inner sleeve 9, the outer sleeve 10, and the fixing sheet 12 are prepared by 3D printing technology, and the material is selected from one of plastic, stainless steel, and resin, and is preferably resin; the material of the spring 11 is selected to be stainless steel. As an example, the wire diameter of the spring 11 is 0.5-0.6 mm, the outer diameter is 6-8 mm, and the height is 30-40 mm; the spring 11 has an elastic coefficient of 0.2-1.6 N / mm; the thickness of the fixing sheet 12 is less than 2 mm.

[0072] In a possible implementation, the boundary node 4 in FIG. 3 is a cylindrical structure, so as to reduce the damping of the whole structure. FIG. 7 shows a schematic diagram of a three-dimensional structure of a boundary node according to an embodiment of the present disclosure. As shown in FIG. 7, the boundary node 4 is formed by a plurality of cylinders with different diameters arranged in an axial direction, a circular ring-shaped support is formed at the interface between adjacent cylinders, and a through hole is formed in the center of one of the cylinders. For example, the diameter of the through hole in the center of the boundary node 4 is 6.6-8.6 mm, and is preferably 7.6 mm. For example, the diameter of the protrusion at the bottom of the boundary node 4 is 11-13 mm, and is preferably 12 mm. For example, the maximum displacement of the boundary node 4 is 20-30 mm. For example, the boundary node 4 can be prepared by a 3D printing technology, and the material is selected from one of plastic, stainless steel and resin, and is preferably resin.

[0073] In a possible implementation, the boundary node 4 in FIG. 3 is a cylindrical structure, so as to reduce the damping of the whole structure. FIG. 7 shows a schematic diagram of a three-dimensional structure of a boundary node according to an embodiment of the present disclosure. As shown in FIG. 7, the boundary node 4 is formed by a plurality of cylinders with different diameters arranged in an axial direction, a circular ring-shaped support is formed at the interface between adjacent cylinders, and a through hole is formed in the center of one of the cylinders. For example, the diameter of the through hole in the center of the boundary node 4 is 6.6-8.6 mm, and is preferably 7.6 mm. For example, the diameter of the protrusion at the bottom of the boundary node 4 is 11-13 mm, and is preferably 12 mm. For example, the maximum displacement of the boundary node 4 is 20-30 mm. For example, the boundary node 4 can be prepared by a 3D printing technology, and the material is selected from one of plastic, stainless steel and resin, and is preferably resin.

[0074] As shown in FIG. 7 and FIG. 8, the bottom end of the boundary node 4 is provided with an additional cylindrical protrusion compared with the internal node 5. By matching the protrusion at the bottom of the boundary node 4 with the blind hole of the loading plate 8, the displacement load applied to the boundary node 4 in the two-dimensional truss structure platform 20 can be realized, and the size of the displacement load applied can be changed only by adjusting the position of the blind hole on the loading plate 8.

[0075] It should be noted that the two-dimensional truss structure platform 20 shown in FIG. 2 is only an example, and the user can configure the structure of the two-dimensional truss structure platform 20 according to needs. For example, different two-dimensional truss structure platforms 20 can be constructed by adjusting the values of M and N. Specifically, increasing the values of M and N can improve the measurement accuracy, and reducing the values of M and N is conducive to the miniaturization of the device, and thus the non-Hermitian system ultra-sensitivity detection method provided by the embodiments of the present disclosure can be used to realize accurate measurement of the energy spectrum of a static non-Hermitian system with any boundary disturbance and any degree of freedom.

[0076] The non-Hermitian system ultra-sensitivity detection method provided by the embodiments of the present disclosure will be described in detail below.

[0077] FIG. 9 shows a flowchart of a method for detecting super-sensitivity of a non-Hermite system according to an embodiment of the present disclosure. The method can be performed by the control device 100 in FIG. 1. As shown in FIG. 9, the method can include:

[0078] At step 901, different displacement loads are sequentially applied to boundary nodes in a two-dimensional truss structure platform, which are used as boundary condition disturbances to excite eigenstates of a target two-dimensional static non-Hermite system. Different displacement loads excite different eigenstates.

[0079] The two-dimensional truss structure platform is used to simulate the target two-dimensional static non-Hermite system. The two-dimensional truss structure platform includes a plurality of boundary nodes, a plurality of internal nodes, and a plurality of connecting rods. The plurality of boundary nodes are used to simulate the boundary of the target two-dimensional static non-Hermite system, and the plurality of internal nodes are used to simulate the interior of the target two-dimensional static non-Hermite system. Any internal node is coupled to at least one boundary node through at least one connecting rod. As an example, the two-dimensional truss structure platform can be the two-dimensional truss structure platform 20 in FIG. 1.

[0080] As an example, the plurality of boundary nodes and the plurality of internal nodes are arranged in M*N. M represents the number of nodes arranged in the first direction, and N represents the number of nodes arranged in the second direction. Both M and N are integers greater than 2. The specific values of M and N can be set as needed, and are not limited. For example, M can be set to 12 and N can be set to 3, and a two-dimensional truss structure platform 20 as shown in FIGS. 2 and 3 can be constructed in advance.

[0081] As an example, the two-dimensional truss structure platform further includes a base and a plurality of slide rods. The plurality of slide rods are arranged along the second direction. The plurality of boundary nodes and the plurality of internal nodes are connected to the base through the plurality of slide rods to limit the movement of the plurality of internal nodes and the plurality of boundary nodes in the second direction. The base is used to support the plurality of slide rods, the plurality of connecting rods, the plurality of internal nodes, and the plurality of boundary nodes.

[0082] The displacement load represents the internal force generated by the structure member (such as the connecting rod) in the two-dimensional truss structure platform in the form of forced displacement of the boundary node. This displacement is called displacement load.

[0083] Exemplarily, the displacement load applied to each boundary node in the two-dimensional truss structure platform can be controlled multiple times, wherein the displacement load applied to each boundary node in the two-dimensional truss structure platform is different at least in one time. In this way, the eigenstate corresponding to one eigenvalue of the target two-dimensional static non-Hermitian system can be excited by applying the displacement load as a boundary condition disturbance to each boundary node in the two-dimensional truss structure platform each time, and the eigenstates corresponding to multiple eigenvalues of the target two-dimensional static non-Hermitian system can be excited in turn by applying the displacement load as different boundary condition disturbances to each boundary node in the two-dimensional truss structure platform multiple times, so as to realize the excitation of the eigenstate of the non-Hermitian system with arbitrary boundary condition disturbance. In addition, the displacement load is applied to each boundary node in the two-dimensional truss structure platform simulating the target two-dimensional static non-Hermitian system multiple times for different degrees of freedom of the target two-dimensional static non-Hermitian system, so as to realize the excitation of the eigenstate of the non-Hermitian system with arbitrary boundary condition disturbance and arbitrary degree of freedom. The eigenstate refers to a specific state of a physical system, and when a certain physical quantity of the physical system is measured, the physical quantity has a certain value, and this state is called the eigenstate of the physical quantity.

[0084] Exemplarily, the displacement load applied to each boundary node in the two-dimensional truss structure platform can be controlled multiple times, wherein the displacement load applied to each boundary node in the two-dimensional truss structure platform can be the same or different each time, and no limitation is made in this regard.

[0085] Exemplarily, the displacement load to be applied to each boundary node in the two-dimensional truss structure platform can be determined in advance, and then the position of each boundary node can be adjusted according to the displacement load to be applied to each boundary node, so as to apply the displacement load to each boundary node. As an example, the two-dimensional truss structure platform is provided with a loading plate, the loading plate is placed in the groove of the base, a plurality of blind holes are formed on the loading plate, and each blind hole is matched with one boundary node. For any boundary node, the position of the boundary node can be changed by controlling the position of the corresponding blind hole on the loading plate, so as to apply the displacement load to be applied to the boundary node.

[0086] In a possible implementation, before the step 901 is performed, the displacement load to be applied to each boundary node in the two-dimensional truss structure platform corresponding to any eigenstate ψ of the target two-dimensional static non-Hermitian system can be determined, wherein the displacement load to be applied to each boundary node coupled with an internal node is the component or λ 2a component of the eigenstate ψ, where λ represents an eigenvalue corresponding to the eigenstate ψ. As an example, a two-dimensional truss structure platform is shown in FIG. 2 and FIG. 3 as described above, where each boundary node of the upper boundary, each boundary node of the lower boundary, each boundary node of the left boundary, and each boundary node of the right boundary are coupled with the internal nodes, and the displacement load to be applied to the boundary nodes of the upper boundary, the upper boundary nodes of the left boundary, the upper boundary nodes of the right boundary, and the lower boundary nodes of the left boundary can be configured as a component of the eigenstate ψ, or λ 2 a component of the eigenstate ψ; as an example, the displacement load to be applied to each boundary node of the upper boundary, each boundary node of the left boundary, and each boundary node of the right boundary can be configured as a component of the eigenstate ψ, i.e., the displacement load to be applied to each boundary node arranged in the horizontal direction in FIG. 2 when n = 0 can be configured as a component of the eigenstate ψ; the displacement load to be applied to each boundary node of the lower boundary, each boundary node of the left boundary, and each boundary node of the right boundary can be configured as λ 2 a component of the eigenstate ψ, i.e., the displacement load to be applied to each boundary node arranged in the horizontal direction in FIG. 2 when n = 2 can be configured as λ 2 a component of the eigenstate ψ. As an example, the displacement load to be applied to each boundary node not coupled with the internal nodes can be set according to requirements, for example, can be set to 0. Wherein the components of the eigenstate ψ and λ 2 The components of the eigenstate ψ and λ can be determined by existing methods for calculating the components of the eigenstate, for example, the eigenstate ψ and λ can be calculated respectively 2 a component of the eigenstate ψ, or λ 2 a component of the eigenstate ψ.

[0087] In one possible implementation, the method further includes: determining, for each boundary node at the first boundary, the displacement load to be applied to the boundary node as the (a-1)th to (M+a-2)th components of the eigenstate ψ in sequence, where the value of a is determined by the unit structure of the target two-dimensional static non-Hermitian system; as an example, for a two-dimensional truss structure platform with s nodes in each unit cell, a = s+1, for example, a = 3 in the above FIG. 2; and determining, for each boundary node at the second boundary, the displacement load to be applied to the boundary node as λ 2the a-1th to the M+a-2th components of ψ; wherein the first boundary and the second boundary are two boundaries of the two-dimensional truss structure platform along the first direction. As an example, the two-dimensional truss structure platform is shown in FIG. 2 and FIG. 3 as described above, the boundary nodes at the first boundary include the boundary nodes arranged along the horizontal direction when n = 0 in FIG. 2, and the displacement load to be applied to these boundary nodes in order is the a-1th to the M+a-2th components of ψ according to the order of the value of m in FIG. 2 from small to large; the boundary nodes at the second boundary include the boundary nodes arranged along the horizontal direction when n = 2 in FIG. 2, and the displacement load to be applied to these boundary nodes in order is λ 2 the a-1th to the M+a-2th components of ψ.

[0088] In a possible implementation, the determining, for each boundary node at the first boundary, the displacement load to be applied to the boundary node in order as the a-1th to the M+a-2th components of ψ, includes: determining, for each boundary node at the first boundary, a first displacement load to be applied to the boundary node in order as the real part of the a-1th to the M+a-2th components of ψ, and a second displacement load to be applied to the boundary node in order as the imaginary part of the a-1th to the M+a-2th components of ψ; and the determining, for each boundary node at the second boundary, the displacement load to be applied to the boundary node in order as λ 2 the a-1th to the M+a-2th components of ψ, includes: the determining, for each boundary node at the second boundary, a first displacement load to be applied to the boundary node in order as λ 2 the real part of the a-1th to the M+a-2th components of ψ, and a second displacement load to be applied to the boundary node in order as λ 2 the imaginary part of the a-1th to the M+a-2th components of ψ. In this way, the real part and the imaginary part of the components of the eigenstate ψ are respectively determined as the displacement load (i.e., the first displacement load and the second displacement load) to be applied to each boundary node at the first boundary twice, and the real part and the imaginary part of the components of λ 2 the real part and the imaginary part of the components of the eigenstate ψ are respectively determined as the displacement load (i.e., the first displacement load and the second displacement load) to be applied to each boundary node at the second boundary twice, wherein the displacement load to be applied to different boundary nodes at the same time is the eigenstate ψ or λ 2 the real part of the components of the eigenstate ψ, or the imaginary part of the components of the eigenstate ψ, or the real part of the components of λ, or the imaginary part of the components of λ. 2imaginary parts of the a-1th to M+a-2th components of the eigenstate ψ; and the second displacement load (i.e., the second displacement load) is the imaginary part of the a-1th to M+a-2th components of the eigenstate ψ in turn. The boundary nodes at the second boundary include the boundary nodes arranged along the horizontal direction when n = 2 in FIG. 2; and these boundary nodes determine the two displacement loads to be applied in turn according to the order from small to large of the values of m in FIG. 2, wherein the displacement load to be applied once (i.e., the first displacement load) is the real part of the a-1th to M+a-2th components of the eigenstate ψ in turn, and the displacement load to be applied once (i.e., the second displacement load) is the imaginary part of the a-1th to M+a-2th components of the eigenstate ψ in turn. 2 imaginary parts of the a-1th to M+a-2th components of the eigenstate ψ; and the second displacement load (i.e., the second displacement load) is the imaginary part of the a-1th to M+a-2th components of the eigenstate ψ in turn. The boundary nodes at the second boundary include the boundary nodes arranged along the horizontal direction when n = 2 in FIG. 2; and these boundary nodes determine the two displacement loads to be applied in turn according to the order from small to large of the values of m in FIG. 2, wherein the displacement load to be applied once (i.e., the first displacement load) is the real part of the a-1th to M+a-2th components of the eigenstate ψ in turn, and the displacement load to be applied once (i.e., the second displacement load) is the imaginary part of the a-1th to M+a-2th components of the eigenstate ψ in turn. 2 imaginary parts of the a-1th to M+a-2th components of the eigenstate ψ; and the second displacement load (i.e., the second displacement load) is the imaginary part of the a-1th to M+a-2th components of the eigenstate ψ in turn. The boundary nodes at the second boundary include the boundary nodes arranged along the horizontal direction when n = 2 in FIG. 2; and these boundary nodes determine the two displacement loads to be applied in turn according to the order from small to large of the values of m in FIG. 2, wherein the displacement load to be applied once (i.e., the first displacement load) is the real part of the a-1th to M+a-2th components of the eigenstate ψ in turn, and the displacement load to be applied once (i.e., the second displacement load) is the imaginary part of the a-1th to M+a-2th components of the eigenstate ψ in turn.

[0089] The step 902 detects the displacement field of the internal nodes in the two-dimensional truss structure platform under the different displacement loads.

[0090] In the step 901, the target two-dimensional static non-Hermitian system is in an eigenstate of an eigenvalue, and the internal nodes will displace in response to the displacement load applied to the boundary nodes. Therefore, the displacement field of the internal nodes in the two-dimensional truss structure platform can be detected, and the eigenvalue can be determined based on the detected displacement field of the internal nodes.

[0091] In a possible implementation, the step of detecting the displacement field of the internal nodes in the two-dimensional truss structure platform under the different displacement loads includes: detecting a first displacement field of the internal nodes in the two-dimensional truss structure platform when the corresponding first displacement load is applied to each boundary node at the first boundary and the second boundary; and detecting a second displacement field of the internal nodes in the two-dimensional truss structure platform when the corresponding second displacement load is applied to each boundary node at the first boundary and the second boundary. In this way, the first displacement field and the second displacement field of the internal nodes in the two-dimensional truss structure platform are detected when the first displacement load and the second displacement load are applied to each boundary node of the two-dimensional truss structure platform, respectively.

[0092] In a possible implementation, the displacement field of the internal nodes in the two-dimensional truss structure platform can be measured by using a digital image correlation method (Digital Image Correlation, DIC). The digital image correlation method is a non-contact optical measurement technology, which is widely used to measure the displacement field and deformation of the surface of an object. The digital image correlation method determines the displacement and strain of the surface of the internal nodes by comparing images of the internal nodes in different states. Specifically, a group of initial images can be taken before each time the displacement load is applied to the boundary nodes in the two-dimensional truss structure platform. These images will be used as a reference for subsequent comparison. Then, the displacement load is applied to the boundary nodes in the two-dimensional truss structure platform, so that the internal nodes are deformed. After the internal nodes are deformed, a group of deformation images corresponding to the initial images is taken. The existing digital image correlation software is used to register the deformation images and the initial images. For example, the feature points can be identified and matched. By comparing the positions of the feature points in the initial images and the deformation images, the displacement of each internal node is calculated.

[0093] In step 903, eigenvalues corresponding to different eigenstates are determined based on the displacement field of the internal nodes in the two-dimensional truss structure platform.

[0094] In a possible implementation, the determination of the eigenvalues corresponding to different eigenstates based on the displacement field of the internal nodes in the two-dimensional truss structure platform includes: for any eigenstate ψ, the real part and the imaginary part of the eigenvalue λ corresponding to the eigenstate ψ are determined based on the displacement field of the internal nodes in the two-dimensional truss structure platform and the eigenstate ψ, so as to obtain the eigenvalue λ. In this way, after the displacement load is applied to the boundary nodes in the two-dimensional truss structure platform each time, the real part and the imaginary part of the corresponding eigenvalue λ can be extracted based on the detected displacement field of the internal nodes in the two-dimensional truss structure platform and the eigenstate ψ, so as to determine the corresponding eigenvalue.

[0095] In a possible implementation, the determination of the real part and the imaginary part of the eigenvalue λ corresponding to the eigenstate ψ based on the displacement field of the internal nodes in the two-dimensional truss structure platform and the eigenstate ψ includes: the real part and the imaginary part of the eigenvalue λ are calculated based on the first displacement field, the second displacement field, the first displacement load applied to each boundary node at the first boundary, and the second displacement load applied to each boundary node at the first boundary and the second boundary.

[0096] For example, the real part and the imaginary part of the eigenvalue, the first displacement field, the second displacement field, the first displacement load applied to each boundary node at the first boundary and the second boundary, and the second displacement load applied to each boundary node at the first boundary and the second boundary satisfy the following relationship: r = λR Re(ψ)-λ I Im(ψ) ψ i =λ R Im(ψ)+λ I Re(ψ)

[0097] wherein, λ R and λ I respectively represent the real part and the imaginary part of the eigenvalue λ, Re(ψ) represents the real part of the eigenstate ψ, i.e. the first displacement load applied by each boundary node at the first boundary; Im(ψ) represents the imaginary part of the eigenstate ψ, i.e. the second displacement load applied by each boundary node at the first boundary; ψ r represents the first displacement field of the internal node, ψ i is the second displacement field of the internal node. Since Re(ψ) and Im(ψ) are known quantities, ψ r and ψ i can be detected, and Re(ψ), Im(ψ), ψ r and ψ i are substituted into the above formula to obtain the real part λ R and the imaginary part λ I of the eigenvalue λ.

[0098] Since the two-dimensional truss structure platform includes multiple internal nodes, for each internal node, a certain component of the corresponding first displacement field and second displacement field can be measured, and then the real part and the imaginary part of the eigenvalue λ can be obtained through the above formula. In this way, under a certain eigenstate, multiple solutions of the real part and the imaginary part of the eigenvalue λ corresponding to the eigenstate can be obtained through multiple internal nodes, and then the reliability of the experimentally measured real part and imaginary part of the eigenvalue λ can be verified through the consistency condition of these solutions.

[0099] Step 904, determining the quantitative relationship between the boundary condition perturbation and the energy spectrum response of the target two-dimensional static non-Hermitian system based on the different displacement loads and the eigenvalues corresponding to different eigenstates; wherein, the energy spectrum response includes multiple eigenvalues.

[0100] Through the steps 901-903, based on the displacement field of the internal nodes in the two-dimensional truss structure platform detected when the displacement load is applied to the boundary nodes in the two-dimensional truss structure platform multiple times, the plurality of eigenvalues can be determined. In this way, by changing the displacement load applied to the boundary nodes in the two-dimensional truss structure platform, the measurement of all eigenvalues of the target two-dimensional static non-Hermitian system is realized, thereby realizing the measurement of all eigenvalues of the non-Hermitian system with arbitrary equivalent boundary conditions and equivalent degrees of freedom, which constitute the energy spectrum of the target two-dimensional static non-Hermitian system. Further, in step 904, by inductively processing the above measurement results, a quantitative relationship between the boundary condition disturbance and the energy spectrum response of the target two-dimensional static non-Hermitian system is established, thereby accurately characterizing the sensitivity of the energy spectrum of the target two-dimensional static non-Hermitian system.

[0101] In a possible implementation, the determining of the quantitative relationship between the boundary condition disturbance and the energy spectrum response of the target two-dimensional static non-Hermitian system further includes: obtaining a quantitative relationship between a boundary condition disturbance corresponding to different degrees of freedom and an energy spectrum response of the target two-dimensional static non-Hermitian system in a case where the target two-dimensional static non-Hermitian system has the different degrees of freedom; and determining a quantitative relationship between the degrees of freedom, the boundary condition disturbance and the energy spectrum response of the target two-dimensional static non-Hermitian system based on the different degrees of freedom and the quantitative relationship between the boundary condition disturbance corresponding to the different degrees of freedom and the energy spectrum response of the target two-dimensional static non-Hermitian system. Illustratively, for different degrees of freedom, the displacement load applied to each boundary node in the two-dimensional truss structure platform can be changed to simulate different degrees of freedom of the target two-dimensional static non-Hermitian system, thereby realizing the simulation of any degree of freedom of the target two-dimensional static non-Hermitian system. Further, for each target two-dimensional static non-Hermitian system, the steps 901-903 are performed to completely measure the energy spectrum response of the non-Hermitian system with arbitrary degrees of freedom and arbitrary boundary condition disturbances, and further to determine the quantitative relationship between the boundary condition disturbance and the energy spectrum response of the target two-dimensional static non-Hermitian system of the degree of freedom. The quantitative relationships between the boundary condition disturbances and the energy spectrum responses of the target two-dimensional static non-Hermitian systems of different degrees of freedom are analyzed to establish a quantitative relationship between the boundary condition disturbance, the degree of freedom and the energy spectrum response of the corresponding non-Hermitian system, thereby quantitatively characterizing the sensitivity of the energy spectrum of the non-Hermitian system.

[0102] In the embodiments of the present disclosure, different displacement loads are sequentially applied to boundary nodes in a two-dimensional truss structure platform, and the displacement loads are used as boundary condition disturbances to excite eigenstates of a target two-dimensional static non-Hermitian system. Different displacement loads excite different eigenstates. The two-dimensional truss structure platform is used to simulate the target two-dimensional static non-Hermitian system, and the two-dimensional truss structure platform includes a plurality of boundary nodes, a plurality of internal nodes, and a plurality of connecting rods. The plurality of boundary nodes are used to simulate the boundary of the target two-dimensional static non-Hermitian system, and the plurality of internal nodes are used to simulate the interior of the target two-dimensional static non-Hermitian system. Any internal node is coupled to at least one boundary node through at least one connecting rod. In this way, the boundary condition disturbances and the degrees of freedom of the target two-dimensional static non-Hermitian system can be configured as needed, and then the target two-dimensional static non-Hermitian system with arbitrary boundary condition disturbances and arbitrary degrees of freedom can be simulated by using a two-dimensional truss structure platform with a limited size that is constructed in advance. Thus, the energy spectrum response of an equivalent one-dimensional dynamic non-Hermitian system with arbitrary degrees of freedom under the action of boundary condition disturbances can be detected. At the same time, since the two-dimensional truss structure platform is formed by pure mechanical elements cooperating with each other, there is no need for energy gain and dissipation or external active driving, thereby greatly reducing the complexity of the experiment compared with the existing spectrum measurement method based on a non-conservative dynamic non-Hermitian system. Moreover, since the two-dimensional truss structure platform belongs to a static system, it has stronger robustness to disturbances such as damping or structural defects. In addition, the displacement of the internal nodes is macroscopic, with a scale of centimeters, so that the accuracy and stability of the experimental measurement are higher. Then, the displacement field of the internal nodes in the two-dimensional truss structure platform under the different displacement loads is detected. Based on the displacement field of the internal nodes in the two-dimensional truss structure platform, eigenvalues corresponding to different eigenstates are determined. Thus, the eigenenergy spectrum of the non-Hermitian system with arbitrary boundary condition disturbances and arbitrary degrees of freedom can be accurately measured. Finally, based on the different displacement loads and the eigenvalues corresponding to different eigenstates, a quantitative relationship between the boundary condition disturbances and the energy spectrum response of the target two-dimensional static non-Hermitian system is determined. As an example, a quantitative relationship between the energy spectrum response of the target two-dimensional static non-Hermitian system and the degrees of freedom and the boundary condition disturbances of the target two-dimensional static non-Hermitian system can be established. Thus, a basis for quantitatively analyzing the disturbance sensitivity of the energy spectrum of the non-Hermitian system is provided, and support for designing and manufacturing an ultra-sensitive non-Hermitian sensor is provided. Exemplarily, the non-Hermitian sensor can be a sensor constructed based on an equivalent one-dimensional dynamic non-Hermitian system simulated by a two-dimensional truss structure platform, for example, a sensor for measuring physical quantities such as angle, velocity, translation, liquid level, etc. The displacement loads applied to each boundary node represent the disturbance of the boundary conditions of the non-Hermitian sensor caused by the change of these physical quantities, which causes the eigenstate to change.

[0103] The embodiments of the present disclosure overcome the difficulties in the prior art, such as complicated experimental procedures, low measurement accuracy and stability, and difficult to manipulate boundary conditions and degrees of freedom, and effectively improve the sensitivity of the non-Hermitian system energy spectrum detection.

[0104] The following will illustrate the above-mentioned non-Hermitian system super-sensitivity detection method by taking three exemplary scenarios as examples. FIG. 10 shows a schematic diagram of the attenuation spectrum distribution under the periodic boundary condition according to an embodiment of the present disclosure; FIG. 11 shows the detection results of the energy spectrum of the target two-dimensional static non-Hermitian system in scenario one, scenario two and scenario three according to an embodiment of the present disclosure.

[0105] Scenario one,

[0106] Suppose that the target two-dimensional static non-Hermitian system has a periodic boundary condition in the horizontal direction, according to the Bloch theorem, the displacement field of the internal nodes in the two-dimensional truss structure platform can be written as wherein, represents the displacement of the i-th internal node in the unit cell (m, n), m represents the coordinate value of the unit cell in the vertical direction, n represents the coordinate value of the unit cell in the horizontal direction, i = 1, 2, λ is the attenuation factor of the displacement field along the vertical direction, which is the eigenvalue of the target two-dimensional static non-Hermitian system, q is the Bloch wave number along the horizontal direction, p i is the polarization component of each internal node. The function relationship between λ and q can be solved by substituting the displacement field into the balance equation of the node, which is called the attenuation spectrum. Exemplarily, the displacement field is brought into the static equilibrium equations of the two nodes in a single unit cell, and the two algebraic equations can be converted into a homogeneous matrix equation about the polarization component p i . Thus, the function relationship between the attenuation factor λ and the wave number q, i.e., the attenuation spectrum, can be determined by the condition that the determinant of the coefficient matrix of the matrix equation is zero, and the polarization components p1 and p2 can be obtained by solving the kernel space of the coefficient matrix; let the coupling stiffness k1 = 4, k2 = 0.5, k3 = k4 = 1, and the two attenuation spectra are connected at the beginning and end on the complex plane (Re(λ), Im(λ)) to form a ring-like topological structure, as shown in FIG. 10.

[0107] The target two-dimensional static non-Hermitian system can be controlled to continuously transit from a periodic boundary condition to an open boundary condition. Let Δ∈[0, 1] be a perturbation factor of the boundary condition. When Δ=1, the non-Hermitian system is in a periodic boundary condition, and when Δ=0, the non-Hermitian system is in an open boundary condition. Different values of the perturbation factor correspond to displacement loads applied to the boundary nodes. Therefore, the simulated target two-dimensional static non-Hermitian system in the two-dimensional truss structure platform can be continuously transited from a periodic boundary condition to an open boundary condition by adjusting the displacement loads applied to the boundary nodes in the two-dimensional truss structure platform. Since the non-Hermitian system is extremely sensitive to the boundary condition, even a very small perturbation of the boundary condition will cause a significant change in the decay spectrum when the non-Hermitian system has a sufficient number of degrees of freedom. This is the basis for using a non-Hermitian system to achieve ultra-sensitive sensing. Since the translation symmetry of the non-Hermitian system is broken under a non-periodic boundary condition, the decay spectrum can only be obtained by diagonalizing the stiffness matrix in the real space.

[0108] The displacement loads applied to the boundary nodes in the two-dimensional truss structure platform can be adjusted to simulate a target two-dimensional static non-Hermitian system with degrees of freedom. The solid line in FIG. 11 shows the evolution process of the imaginary part of the pure imaginary eigenvalue (i.e., λ=iκ, i represents the imaginary unit) when Δ continuously increases from 10 -16 . The eigenstate corresponding to the eigenvalue is denoted as ψ. Obviously, when the perturbation Δ of the boundary condition is very small, the imaginary part of the eigenvalue does not respond. Only when Δ reaches 10 -3 , κ becomes non-zero (about 4.3%), which indicates that the perturbation sensitivity of the target two-dimensional static non-Hermitian system with degrees of freedom is on the order of 10 -3 .

[0109] Based on the two-dimensional truss structure platform 20 shown in FIG. 2 or FIG. 3, the eigenvalue is measured by using the ultra-sensitive detection method of the non-Hermitian system provided in the above embodiments. Exemplarily, first, the 2nd to 13th elements of the real part of the eigenstate ψ (denoted as Re(ψ)) are taken as the displacement loads of the nodes at n=0 (including the 10 upper boundary nodes 4 and the 2 left and right boundary nodes 4), the 2nd to 13th elements of the real part of ψλ 2 are taken as the displacement loads of the nodes at n=2 (including the 10 lower boundary nodes 4 and the 2 left and right boundary nodes 4), and then the displacement field of the internal nodes 5 is measured and denoted as ψ r ; then the 2nd to 13th elements of the imaginary part of the eigenstate ψ (denoted as Im(ψ)) are taken as the displacement loads of the nodes at n=0, the 2nd to 13th elements of the imaginary part of ψλ 2 are taken as the displacement loads of the nodes at n=2, and then the displacement field of the internal nodes 5 is measured and denoted as ψ i .

[0110] By definition, ψ r With ψ i Satisfying the following relationship: ψ r =λ R Re(ψ)-λ I Im(ψ) ψ i =λ R Im(ψ)+λ I Re(ψ)

[0111] Where λ R With λ I Let Re(ψ), Im(ψ), and ψ represent the real and imaginary parts of λ, respectively. r and ψ i All quantities are known; the above vector equations give 10 sets of values ​​for λ. R and λ I A system of two linear equations in two variables can be solved by solving any set of equations to obtain a solution. j = 1, 2, ..., 10, and these 10 sets of solutions should be consistent, which can be used to verify the reliability of the measurement results.

[0112] The square scatter plots in Figure 11 show the imaginary part of the eigenvalues ​​simulated by the above-mentioned detection method for the ultrasensitivity of non-Hermitian systems as Δ increases. These values ​​agree very well with the theoretical values, successfully capturing the equivalent degrees of freedom. Non-Hermitian systems 10 -3 Sensitivity to disturbances of a certain magnitude.

[0113] Scene 2

[0114] Using the same conditions as in Scenario 1, the displacement loads applied to the boundary nodes of the two-dimensional truss structure platform are adjusted to simulate the degrees of freedom of the target two-dimensional static non-Hermitian system. The dashed line in Figure 11 illustrates the evolution of κ with respect to Δ. Due to the increase in equivalent degrees of freedom, the sensitivity of the energy spectrum of the non-Hermitian system significantly improves; for example, only when Δ increases to 10... -9 When the order of magnitude is 10, κ exhibits a non-zero response, while when Δ = 10 -3 At that time, κ had reached 75% of the periodic boundary condition, compared to A significant increase. The circular scatter plots in Figure 11 show the results obtained through simulation using a two-dimensional truss structure platform, which agrees very well with the theoretical values, successfully capturing the [data / data]. Non-Hermitian systems 10 -9 Sensitivity to disturbances of a certain magnitude.

[0115] Scene 3

[0116] With the same conditions as in scenario one, the displacement load applied on the boundary nodes in the two-dimensional truss platform is adjusted to simulate the degrees of freedom of the target two-dimensional static non-Hermitian system The dotted line in FIG. 11 shows the evolution of κ with Δ. At this time, the sensitivity of the non-Hermitian system energy spectrum is further enhanced, reaching the order of 10 -15 The triangular scatter points in FIG. 11 show the results measured by simulating the two-dimensional truss platform, which are in good agreement with the theoretical values, successfully capturing the perturbation sensitivity of the non-Hermitian system 10 -15 The order of magnitude.

[0117] Based on the same inventive concept of the above method embodiments, the embodiments of the present disclosure also provide a non-Hermitian system super-sensitivity detection device, which can be used to execute the technical solutions described in the above non-Hermitian system super-sensitivity detection method embodiments.

[0118] FIG. 12 shows a structural schematic diagram of a non-Hermitian system super-sensitivity detection device according to an embodiment of the present disclosure. As shown in FIG. 12, the device can include: a displacement load module 1201 for controlling different displacement loads to be sequentially applied to the boundary nodes in the two-dimensional truss platform, the displacement load being used as a boundary condition perturbation to excite the eigenstates of the target two-dimensional static non-Hermitian system, and different displacement loads exciting different eigenstates; wherein the two-dimensional truss platform is used to simulate the target two-dimensional static non-Hermitian system, and the two-dimensional truss platform includes a plurality of boundary nodes, a plurality of internal nodes, and a plurality of connecting rods; the plurality of boundary nodes are used to simulate the boundary of the target two-dimensional static non-Hermitian system, the plurality of internal nodes are used to simulate the interior of the target two-dimensional static non-Hermitian system, and any internal node is coupled to at least one boundary node in the plurality of boundary nodes through at least one connecting rod in the plurality of connecting rods; a detection module 1202 for detecting the displacement field of the internal nodes in the two-dimensional truss platform under the different displacement loads; the detection module 1202 is also used to determine the eigenvalues corresponding to different eigenstates based on the displacement field of the internal nodes in the two-dimensional truss platform; an analysis module 1203 for determining the quantitative relationship between the boundary condition perturbation and the energy spectrum response of the target two-dimensional static non-Hermitian system based on the different displacement loads and the eigenvalues corresponding to different eigenstates; wherein the energy spectrum response includes a plurality of eigenvalues.

[0119] ​In the embodiments of the present disclosure, different displacement loads are sequentially applied to boundary nodes in a two-dimensional truss structure platform, and the displacement loads are used as boundary condition disturbances to excite eigenstates of a target two-dimensional static non-Hermitian system. Different displacement loads excite different eigenstates. The two-dimensional truss structure platform is used to simulate the target two-dimensional static non-Hermitian system, and the two-dimensional truss structure platform includes a plurality of boundary nodes, a plurality of internal nodes, and a plurality of connecting rods. The plurality of boundary nodes are used to simulate the boundary of the target two-dimensional static non-Hermitian system, and the plurality of internal nodes are used to simulate the interior of the target two-dimensional static non-Hermitian system. Any internal node is coupled to at least one boundary node through at least one connecting rod. In this way, the boundary condition disturbances in the two-dimensional truss structure platform and the degrees of freedom of the target two-dimensional static non-Hermitian system can be configured as needed. The two-dimensional truss structure platform with a limited size is used to simulate the target two-dimensional static non-Hermitian system with arbitrary boundary condition disturbances and arbitrary degrees of freedom, so as to detect the energy spectrum response of an equivalent one-dimensional non-Hermitian system with arbitrary degrees of freedom under the action of boundary condition disturbances. At the same time, since the two-dimensional truss structure platform is formed by pure mechanical elements, it does not need energy gain and dissipation or external active driving, so it can simulate a static non-Hermitian system with arbitrary adjustable boundary conditions and arbitrary degrees of freedom without energy gain or dissipation, thereby greatly reducing the complexity of the experiment. Since the two-dimensional truss structure platform belongs to a static system, it has stronger robustness to disturbances such as damping or structural defects, and the displacement of the internal nodes is macroscopic with a scale of centimeters, so the accuracy and stability of the experimental measurement are higher. Further, the displacement field of the internal nodes in the two-dimensional truss structure platform under the different displacement loads is detected. Based on the displacement field of the internal nodes in the two-dimensional truss structure platform, eigenvalues corresponding to different eigenstates are determined, so as to realize accurate measurement of the eigenenergy spectrum of the non-Hermitian system with arbitrary boundary condition disturbances and arbitrary degrees of freedom. Finally, based on the different displacement loads and the eigenvalues corresponding to different eigenstates, a quantitative relationship between the boundary condition disturbances and the energy spectrum response of the target two-dimensional static non-Hermitian system is determined. As an example, a quantitative relationship between the energy spectrum response of the target two-dimensional static non-Hermitian system and the degrees of freedom and boundary condition disturbances of the target two-dimensional static non-Hermitian system can be established, thereby providing a basis for quantitatively analyzing the disturbance sensitivity of the energy spectrum of the non-Hermitian system and providing support for designing and manufacturing ultra-sensitive non-Hermitian sensors.

[0120] In a possible implementation, the analysis module 1203 is further configured to: obtain a quantitative relationship between a boundary condition disturbance corresponding to different degrees of freedom and an energy spectrum response of the target two-dimensional static non-Hermitian system in a case where the target two-dimensional static non-Hermitian system has different degrees of freedom; and determine the quantitative relationship between the degrees of freedom, the boundary condition disturbance, and the energy spectrum response of the target two-dimensional static non-Hermitian system based on the different degrees of freedom and the quantitative relationship between the boundary condition disturbance corresponding to the different degrees of freedom and the energy spectrum response of the target two-dimensional static non-Hermitian system.

[0121] In a possible implementation, the displacement load module 1201 is further configured to: determine, based on any eigenstate ψ of the target two-dimensional static non-Hermitian system, a displacement load to be applied to each boundary node in the two-dimensional truss structure platform corresponding to the excitation of the eigenstate ψ; and wherein, for each boundary node coupled with an internal node, the displacement load to be applied is a component of the eigenstate ψ or λ 2 a component of the eigenstate ψ, where λ represents an eigenvalue corresponding to the eigenstate ψ.

[0122] In a possible implementation, the plurality of boundary nodes and the plurality of internal nodes are arranged in M*N, where M represents the number of nodes arranged in a first direction, N represents the number of nodes arranged in a second direction, and M and N are both integers greater than 2; and the displacement load module 1201 is further configured to: for each boundary node at a first boundary, determine the displacement load to be applied to each boundary node as the (a-1)th to (M+a-2)th components of the eigenstate ψ in sequence, where the value of a is determined by a unit structure of the target two-dimensional static non-Hermitian system; and for each boundary node at a second boundary, determine the displacement load to be applied to each boundary node as the (a-1)th to (M+a-2)th components of the eigenstate ψ in sequence; and wherein, the first boundary and the second boundary are two boundaries of the two-dimensional truss structure platform along the first direction. 2

[0123] In a possible implementation, the detection module 1202 is further configured to: for any eigenstate ψ, determine a real part and an imaginary part of an eigenvalue λ corresponding to the eigenstate ψ based on a displacement field of an internal node in the two-dimensional truss structure platform and the eigenstate ψ, to obtain the eigenvalue λ.

[0124] In a possible implementation, the two-dimensional truss structure platform further includes: a base, and a plurality of slide rods, where the plurality of slide rods are arranged along the second direction, and the plurality of boundary nodes and the plurality of internal nodes are connected to the base through the plurality of slide rods to limit the movement of the plurality of internal nodes and the plurality of boundary nodes in the second direction; and the base is configured to carry the plurality of slide rods, the plurality of connecting rods, the plurality of internal nodes, and the plurality of boundary nodes.​

[0125] In a possible implementation, the displacement load module 1201 is further configured to: for each boundary node at the first boundary, determine the first displacement load to be applied to the each boundary node as the real part of the a-1th to M+a-2th components of the eigenstate ψ in sequence, and determine the second displacement load to be applied to the each boundary node as the imaginary part of the a-1th to M+a-2th components of the eigenstate ψ in sequence; for each boundary node at the second boundary, determine the first displacement load to be applied to the each boundary node as the real part of the a-1th to M+a-2th components of the eigenstate ψ in sequence, and determine the second displacement load to be applied to the each boundary node as the imaginary part of the a-1th to M+a-2th components of the eigenstate ψ in sequence; and the detection module 1202 is further configured to: detect the first displacement field of the internal nodes in the two-dimensional truss structure platform when the corresponding first displacement loads are applied to each boundary node at the first boundary and the second boundary; detect the second displacement field of the internal nodes in the two-dimensional truss structure platform when the corresponding second displacement loads are applied to each boundary node at the first boundary and the second boundary; and calculate the real part and the imaginary part of the eigenvalue λ based on the first displacement field, the second displacement field, the first displacement load applied to each boundary node at the first boundary and the second boundary, and the second displacement load applied to each boundary node at the first boundary and the second boundary. 2 ψ in sequence, and determine the second displacement load to be applied to the each boundary node as the imaginary part of the a-1th to M+a-2th components of the eigenstate ψ in sequence; and the detection module 1202 is further configured to: detect the first displacement field of the internal nodes in the two-dimensional truss structure platform when the corresponding first displacement loads are applied to each boundary node at the first boundary and the second boundary; detect the second displacement field of the internal nodes in the two-dimensional truss structure platform when the corresponding second displacement loads are applied to each boundary node at the first boundary and the second boundary; and calculate the real part and the imaginary part of the eigenvalue λ based on the first displacement field, the second displacement field, the first displacement load applied to each boundary node at the first boundary and the second boundary, and the second displacement load applied to each boundary node at the first boundary and the second boundary. 2 ψ in sequence, and determine the second displacement load to be applied to the each boundary node as the imaginary part of the a-1th to M+a-2th components of the eigenstate ψ in sequence; and the detection module 1202 is further configured to: detect the first displacement field of the internal nodes in the two-dimensional truss structure platform when the corresponding first displacement loads are applied to each boundary node at the first boundary and the second boundary; detect the second displacement field of the internal nodes in the two-dimensional truss structure platform when the corresponding second displacement loads are applied to each boundary node at the first boundary and the second boundary; and calculate the real part and the imaginary part of the eigenvalue λ based on the first displacement field, the second displacement field, the first displacement load applied to each boundary node at the first boundary and the second boundary, and the second displacement load applied to each boundary node at the first boundary and the second boundary.

[0126] In some embodiments, the apparatus provided by the embodiments of the present disclosure has functions or includes modules that can be used to perform the methods described in the above method embodiments, and the specific implementation can refer to the description of the above method embodiments. For brevity, details are not repeated here.

[0127] The embodiments of the present disclosure further provide a computer-readable storage medium having computer program instructions stored therein, and the computer program instructions are executed by a processor to implement the above method. The computer-readable storage medium can be a volatile or non-volatile computer-readable storage medium.

[0128] The embodiments of the present disclosure further provide an electronic device, including: a processor; a memory for storing processor-executable instructions; wherein the processor is configured to implement the above method when executing the instructions stored in the memory.

[0129] The embodiments of the present disclosure further provide a computer program product, including computer readable code or a non-volatile computer readable storage medium carrying computer readable code, when the computer readable code is run in the processor of the electronic device, the processor in the electronic device executes the above method.

[0130] FIG. 13 is a block diagram illustrating an electronic device 1900 according to an exemplary embodiment. For example, the electronic device 1900 can be provided as a server or a terminal device. Referring to FIG. 13, the electronic device 1900 includes a processing component 1922, further including one or more processors, and a memory resource represented by a memory 1932, for storing instructions executable by the processing component 1922, such as an application program. The application program stored in the memory 1932 can include one or more than one module each corresponding to a set of instructions. In addition, the processing component 1922 is configured to execute the instructions to perform the above-described method.

[0131] The electronic device 1900 can further include a power supply component 1926 configured to perform power management of the electronic device 1900, a wired or wireless network interface 1950 configured to connect the electronic device 1900 to a network, and an input / output interface 1958 (I / O interface). The electronic device 1900 can operate based on an operating system stored in the memory 1932, such as Windows Server TM , Mac OS X TM , Unix TM , Linux TM , FreeBSD TM or the like.

[0132] In exemplary embodiments, a non-transitory computer readable storage medium, such as the memory 1932 including computer program instructions executable by the processing component 1922 of the electronic device 1900 to perform the above-described method is also provided.

[0133] The present disclosure can be a system, a method, and / or a computer program product. The computer program product can include a computer readable storage medium (or media) having computer readable program instructions thereon for causing a processor to carry out aspects of the present disclosure.

[0134] Computer readable storage media can be tangible storage media which can retain and store instructions for use by an instruction execution device. Computer readable storage media can be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of computer readable storage media include the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanically encoded device such as punch-cards or raised structures in a groove having instructions recorded thereon, and any suitable combination of the foregoing. A computer readable storage medium, as used herein, is not to be construed as being transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., light pulses passing through a fiber-optic cable), or electrical signals transmitted through a wire.

[0135] Computer readable program instructions described herein can be downloaded to respective computing / processing devices from a computer readable storage medium or to an external computer or external storage device via a network, for example, the Internet, a local area network, a wide area network and / or a wireless network. The network can comprise copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers and / or edge servers. A network adapter card or network interface in each computing / processing device receives computer readable program instructions from the network and forwards the computer readable program instructions for storage in a computer readable storage medium within the respective computing / processing device.

[0136] Computer readable program instructions for carrying out operations of the present disclosure can be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, state-setting data, or either source code or object code written in any combination of one or more programming languages, including an object oriented programming language such as Smalltalk, C++ or the like and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The computer readable program instructions can execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer can be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection can be made to an external computer (for example, through the Internet using an Internet Service Provider). In some embodiments, electronic circuitry including, for example, programmable logic circuitry, field-programmable gate array (FPGA), or programmable logic array (PLA) can execute the computer readable program instructions by utilizing state information of the computer readable program instructions to personalize the electronic circuitry, in order to perform aspects of the present disclosure.

[0137] The computer readable program instructions can also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide processes for implementing the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0138] The computer readable program instructions can also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide processes for implementing the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0139] The computer readable program instructions can also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus or other device to produce a computer implemented process such that the instructions which execute on the computer, other programmable data processing apparatus, or other device implement the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0140] The flow diagrams and the block diagrams in the drawings are presented to illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present disclosure. In this regard, each block in the flow diagrams and the block diagrams can represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logic functions. In some alternative implementations, the functions noted in the blocks can occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks can sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and / or flow diagrams, and combinations thereof, can be implemented by special purpose hardware-based systems that perform the specified functions or acts, or combinations of special purpose hardware and

[0141] Embodiments of the present disclosure have been described above, and the description is intended to be illustrative of the embodiments and not restrictive. Many modifications and variations of the described embodiments are possible and are within the scope of the disclosure. The selection of terms is intended to best describe the principles of the embodiments, practical application, or technical improvements in the art, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A method for ultrasensitive detection of non-Hermitian systems, characterized in that, The method comprises: controlling different displacement loads to be applied to boundary nodes in a two-dimensional truss structure platform in turn, the displacement loads being used as boundary condition perturbations for exciting eigenstates of a target two-dimensional static non-Hermitian system, and different displacement loads exciting different eigenstates; wherein the two-dimensional truss structure platform is used for simulating the target two-dimensional static non-Hermitian system, and the two-dimensional truss structure platform comprises a plurality of boundary nodes, a plurality of internal nodes and a plurality of connecting rods; the plurality of boundary nodes are used for simulating boundaries of the target two-dimensional static non-Hermitian system, and the plurality of internal nodes are used for simulating the interior of the target two-dimensional static non-Hermitian system, and any internal node is coupled with at least one boundary node in the plurality of boundary nodes through at least one connecting rod in the plurality of connecting rods; detecting displacement fields of the internal nodes in the two-dimensional truss structure platform under the different displacement loads; determining eigenvalues corresponding to different eigenstates based on the displacement fields of the internal nodes in the two-dimensional truss structure platform; determining a quantitative relationship between the boundary condition perturbations and the energy spectrum response of the target two-dimensional static non-Hermitian system based on the different displacement loads and the eigenvalues corresponding to the different eigenstates; wherein the energy spectrum response comprises a plurality of eigenvalues.

2. The method of claim 1, wherein, The determination of the quantitative relationship between the boundary condition perturbations and the energy spectrum response of the target two-dimensional static non-Hermitian system comprises: obtaining quantitative relationships between boundary condition perturbations corresponding to different degrees of freedom and the energy spectrum response of the target two-dimensional static non-Hermitian system in different degrees of freedom of the target two-dimensional static non-Hermitian system; determining a quantitative relationship between the degrees of freedom, the boundary condition perturbations and the energy spectrum response of the target two-dimensional static non-Hermitian system based on the different degrees of freedom and the quantitative relationships between the boundary condition perturbations corresponding to the different degrees of freedom and the energy spectrum response of the target two-dimensional static non-Hermitian system.

3. The method of claim 1, wherein, The method further comprises: Based on any eigenstate ψ of the target two-dimensional static non-Hermitian system, determine the displacement load to be applied to each boundary node in the two-dimensional truss platform corresponding to the excitation of the eigenstate ψ; wherein each boundary node coupled with an internal node is to be applied a displacement load which is a component or λ 2 of the eigenstate ψ, wherein λ represents an eigenvalue corresponding to the eigenstate ψ.

4. The method of claim 3, wherein, the plurality of boundary nodes and the plurality of internal nodes are arranged in M*N; wherein M represents the number of nodes arranged in a first direction, N represents the number of nodes arranged in a second direction, and M and N are both integers greater than 2; the determination of the displacement load to be applied to each boundary node of the two-dimensional truss structure platform corresponding to the eigenstate ψ comprises: for each boundary node at a first boundary, the displacement load to be applied to each boundary node is determined to be the a-1th to M+a-2th components of the eigenstate ψ in turn, wherein the value of a is determined by a primitive structure of the target two-dimensional static non-Hermitian system; For each boundary node at the second boundary, the displacement load to be applied to the boundary node is determined to be λ 2 the a-1th to M+a-2th components of ψ; wherein the first boundary and the second boundary are two boundaries of the two-dimensional truss structure platform along the first direction.

5. The method of claim 4, wherein, the determination of the eigenvalues corresponding to different eigenstates based on the displacement fields of the internal nodes in the two-dimensional truss structure platform comprises: for any eigenstate ψ, the real part and the imaginary part of the eigenvalue λ corresponding to the eigenstate ψ are determined based on the displacement fields of the internal nodes in the two-dimensional truss structure platform and the eigenstate ψ, so as to obtain the eigenvalue λ.

6. The method of claim 4, wherein, The two-dimensional truss structure platform further comprises a base and a plurality of slide bars, wherein the plurality of slide bars are arranged along the second direction, and the plurality of boundary nodes and the plurality of internal nodes are connected to the base through the plurality of slide bars to limit the movement of the plurality of internal nodes and the plurality of boundary nodes in the second direction; and the base is used to support the plurality of slide bars, the plurality of connecting rods, the plurality of internal nodes and the plurality of boundary nodes.

7. The method of claim 5, wherein, For each boundary node at the first boundary, the displacement load to be applied to the boundary node is sequentially the a-1th to M+a-2th components of the eigenstate ψ, including: For each boundary node at the first boundary, the first displacement load to be applied to the boundary node is sequentially the real part of the a-1th to M+a-2th components of the eigenstate ψ, and the second displacement load to be applied to the boundary node is sequentially the imaginary part of the a-1th to M+a-2th components of the eigenstate ψ; The displacement load to be applied to each boundary node at the second boundary is sequentially λ 2 The a-1th to M+a-2th components of ψ include: the first displacement load to be applied to each boundary node at the second boundary is in turn λ 2 real parts of the a-1th to M+a-2th components of ψ, the second displacement load to be applied is in turn λ 2 imaginary parts of the a-1th to M+a-2th components of ψ The detection of the displacement field of the internal nodes in the two-dimensional truss structure platform under the different displacement loads comprises: detecting a first displacement field of the internal nodes in the two-dimensional truss structure platform when the corresponding first displacement load is applied to each boundary node at the first boundary and the second boundary; detecting a second displacement field of the internal nodes in the two-dimensional truss structure platform when the corresponding second displacement load is applied to each boundary node at the first boundary and the second boundary; For any eigenstate ψ, the real part and the imaginary part of the eigenvalue λ corresponding to the eigenstate ψ are determined based on the displacement field of the internal nodes in the two-dimensional truss structure platform and the eigenstate ψ, including: The real part and the imaginary part of the eigenvalue λ are calculated based on the first displacement field, the second displacement field, the first displacement load applied to each boundary node at the first boundary and the second boundary, and the second displacement load applied to each boundary node at the first boundary and the second boundary.

8. A non-Hermitian system ultra-sensitivity detection device, characterized in that, The device comprises: A displacement load module is configured to control different displacement loads to be sequentially applied to boundary nodes in a two-dimensional truss structure platform, the displacement loads serving as boundary condition perturbations to excite eigenstates of a target two-dimensional static non-Hermitian system, and different displacement loads excite different eigenstates; wherein the two-dimensional truss structure platform is used to simulate the target two-dimensional static non-Hermitian system, and the two-dimensional truss structure platform comprises a plurality of boundary nodes, a plurality of internal nodes and a plurality of connecting rods; the plurality of boundary nodes are used to simulate the boundary of the target two-dimensional static non-Hermitian system, the plurality of internal nodes are used to simulate the interior of the target two-dimensional static non-Hermitian system, and any internal node is coupled to at least one boundary node in the plurality of boundary nodes through at least one connecting rod in the plurality of connecting rods; A detection module is configured to detect a displacement field of the internal nodes in the two-dimensional truss structure platform under the different displacement loads; The detection module is further configured to determine eigenvalues corresponding to different eigenstates based on the displacement field of the internal nodes in the two-dimensional truss structure platform. An analysis module is configured to determine a quantitative relationship between a boundary condition perturbation and an energy spectrum response of the target two-dimensional static non-Hermitian system based on the different displacement loads and the eigenvalues corresponding to different eigenstates, wherein the energy spectrum response includes a plurality of eigenvalues.

9. An electronic device, comprising: The method comprises: a processor; a memory for storing processor-executable instructions; wherein the processor is configured to implement the method of any one of claims 1 to 7 when executing the instructions stored in the memory.

10. A non-transitory computer readable storage medium having stored thereon computer program instructions, wherein, The computer program instructions, when executed by a processor, implement the method of any one of claims 1 to 7.

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