Miloslav Znojil
Complex, non-Hermitian potentials V(x) can often generate standard quantum bound states. H. F. Jones [Phys. Rev. D 78, 065032 (2008)] demonstrated that the idea cannot directly be transferred to scattering. We reveal that a return to the causal and unitary and asymptotically Hermitian scattering theory exists for potentials which are allowed slightly non-local, V=V(x,p).
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We study the scattering problem for the non-Hermitian scattering center, which consists of two Hermitian clusters with anti-Hermitian couplings between them. Counterintuitively, it is shown that it acts as a Hermitian scattering center, satisfying $|r| ^{2}+|t| ^{2}=1$, i.e., the Dirac probability current is conserved, when one of two clusters is embedded in the waveguides. This conclusion can be applied to an arbitrary parity-symmetric real Hermitian graph with additional PT-symmetric potentials, which is more feasible in experiment. Exactly solvable model is presented to illustrate the theor…
We study the possibility of asymmetric transmission induced by a non-Hermitian scattering center embedded in a one-dimensional waveguide, motivated by the aim of realizing quantum diode in a non-Hermitian system. It is shown that a $\mathcal{PT}$ symmetric non-Hermitian scattering center always has symmetric transmission although the dynamics within the isolated center can be unidirectional, especially at its exceptional point. We propose a concrete scheme based on a flux-controlled non-Hermitian scattering center, which comprises a non-Hermitian triangular ring threaded by an Aharonov-Bohm fl…
Non-Hermitian, one-dimensional potentials which are also non-local, allow for scattering asymmetries, namely, asymmetric transmission or reflection responses to the incidence of a particle from left or right. The symmetries of the potential imply selection rules for transmission and reflection. In particular, parity-time (PT) symmetry or the symmetry of any local potential do not allow for asymmetric transmission. We put forward a feasible quantum-optical implementation of non-Hermitian, non-local, non-PT potentials to implement different scattering asymmetries, including transmission asymmetr…
Scattering of a quantum particle from an oscillating barrier or well does not generally conserve the particle energy owing to energy exchange with the photon field, and an incoming particle-free state is scattered into a set of outgoing (transmitted and reflected) free states according to Floquet scattering theory. Here we introduce two families of oscillating non-Hermitian potential wells in which Floquet scattering is fully suppressed for any energy of the incident particle. The scattering-free oscillating potentials are synthesized by application of the Darboux transformation to the time-de…
We investigate the approximate bound state solutions of the Schrödinger equation for the PT-/non-PT-symmetric and non Hermitian Hellmann potential. Exact energy eigenvalues and corresponding normalized wave functions are obtained. Numerical values of energy eigenvalues for the bound states are compared with the ones obtained before. Scattering state solutions are also studied. Phase shifts of the potential are written in terms of the angular momentum quantum number $\ell$.
We explore a way of finding the link between a non-Hermitian Hamiltonian and a Hermitian one. Based on the analysis of Bethe Ansatz solutions for a class of non-Hermitian Hamiltonians and the scattering problems for the corresponding Hermitian Hamiltonians. It is shown that a scattering state of an arbitrary Hermitian lattice embedded in a chain as the scattering center shares the same wave function with the corresponding non-Hermitian tight binding lattice, which consists of the Hermitian lattice with two additional on-site complex potentials, no matter the non-Hermitian is broken PT symmetry…
We investigate the properties of two anti-parity-time (anti-PT )-symmetric four-site scattering centers. The anti-PT -symmetric scattering center may have imaginary couplings, real couplings, and real on-site potentials. The only difference between the two scattering centers is the coupling between two central sites of the scattering center, which plays a crucial role in determining the parity of anti-PT symmetry and significantly affects the scattering properties. For the imaginary coupling, the even-parity anti-PT -symmetric scattering center possesses nonunitary scattering and the differenc…
The complex eigenvalues of some non-Hermitian Hamiltonians, e.g. parity-time symmetric Hamiltonians, come in complex-conjugate pairs. We show that for non-Hermitian scattering Hamiltonians (of a structureless particle in one dimension) possesing one of four certain symmetries, the poles of the $S$-matrix eigenvalues in the complex momentum plane are symmetric about the imaginary axis, i.e. they are complex-conjugate pairs in complex-energy plane. This applies even to states which are not bounded eigenstates of the system, i.e. antibound or virtual states, resonances, and antiresonances. The fo…
Physical relevance of time-independent scattering calculations in non-Hermitian systems: The role of time-growing bound states
本文研究了非厄米系统中不含时散射方法的适用性，指出随时间增长的束缚态会指数放大并主导动力学，导致常规透反射系数失效，强调分析 $S$ 矩阵极点是验证散射计算物理相关性的必要步骤。
The scattering of quantum particles by non-hermitian (generally nonlocal) potentials in one dimension may result in asymmetric transmission and/or reflection from left and right incidence. Eight generalized symmetries based on the discrete Klein's four-group (formed by parity, time reversal, their product, and unity) are used together with generalized unitarity relations to determine the possible and/or forbidden scattering asymmetries. Six basic device types are identified when the scattering coefficients (squared moduli of scattering amplitudes) adopt zero/one values, and transmission and/or…
We complexify a 1-d potential which exhibits bound, reflecting and free states to study various properties of a non-Hermitian system. This potential turns out a PT-symmetric non-Hermitian potential when one of the parameters becomes imaginary. For one PT-symmetric case we have entire real bound state spectrum. Explicit scattering states are constructed to show reciprocity at certain discrete values of energy even though the potential is not parity symmetric. Coexistence of deep energy minima of transmissivity with the multiple spectral singularities (MSS) is observed. We further show that this…
In the framework of the ordinary non-relativistic quantum mechanics, it is known that a quantum particle in a rapidly-oscillating bound potential with vanishing time average can be scattered off or even trapped owing to the phenomenon of dynamical (Kapitza) stabilization. A similar phenomenon occurs for scattering and trapping of optical waves. Such a remarkable result stems from the fact that, even though the particle is not able to follow the rapid external oscillations of the potential, these are still able to affect the average dynamics by means of an effective -albeit small- nonvanishing …
Non-Hermitian scattering in SSH superconducting waveguides: exact Green-function reduction and dimerization-sensitive microwave functionalities
通过精确格林函数约化，将SSH波导环境整合为自能，统一处理非厄米散射、奇异点、相干完美吸收和激射阈值，并分析两种超导器件中的二聚化敏感微波功能。
We investigate the scattering properties of an anti-parity-symmetric non-Hermitian system. The anti-parity-symmetric scattering center possesses imaginary nearest-neighbor hoppings and real onsite potentials, it has been experimentally realized through dissipative coupling and frequency detuning between atomic spin waves. We find that such anti-parity-symmetric system displays three salient features: Firstly, the reflection and transmission are both reciprocal. Secondly, the reflection and transmission probabilities satisfy R+T=1 or R-T=1, which depends on the parity of the scattering center s…
Biorthogonal scattering and generalized unitarity in non-Hermitian systems
研究非厄米特双极系统中双端散射的非互易性和广义单位性，揭示双正交性对恢复单位性的作用及增强传输的物理机制。
We extend the application of the techniques developed within the framework of the pseudo-Hermitian quantum mechanics to study a unitary quantum system described by an imaginary PT-symmetric potential v(x) having a continuous real spectrum. For this potential that has recently been used, in the context of optical potentials, for modelling the propagation of electromagnetic waves travelling in a wave guide half and half filed with gain and absorbing media, we give a perturbative construction of the physical Hilbert space, observables, localized states, and the equivalent Hermitian Hamiltonian. I…
Using techniques of supersymmetric quantum mechanics, scattering properties of Hermitian Hamiltonians, which are related to non-Hermitian ones by similarity transformations, are studied. We have found that the scattering matrix of the Hermitian Hamiltonian coincides with the phase factor of the non-unitary scattering matrix of the non-Hermitian Hamiltonian. The possible presence of a spectral singularity in a non-Hermitian Hamiltonian translates into a pronounced resonance in the scattering cross section of its Hermitian counterpart. This opens a way for detecting spectral singularities in sca…
We study the $\mathcal{PT} $-symmetry breaking for the scattering problem in a one-dimensional (1D) non-Hermitian tight-binding lattice model with balanced gain and loss distributed on two adjacent sites. In the scattering process the system undergoes a transition from the exact $\mathcal{PT} $-symmetry phase to the phase with spontaneously breaking $\mathcal{PT} $-symmetry as the amplitude of complex potentials increases. Using the S-matrix method, we derive an exact discriminant, which can be used to distinguish different symmetry phases, and analytically determine the exceptional point for …
Non-Hermitian systems exhibit many peculiar dynamic behaviors which never showed up in Hermitian systems. The existence of spectral singularity (SS) for a non-Hermitian scattering center provides a lasing mechanism in the context of quantum mechanics. In this paper we show exactly that a finite system at exceptional point (EP) can also provide an alternative laser solution. We investigate the dynamics of non-Hermitian Su-Schrieffer-Heeger (SSH) model around EP, based on the analysis of parity-time (PT ) and chiral-time (CT ) symmetries of the Hamiltonian. In contrast to the SS lasing mechanism…
The conventional bulk-boundary correspondence breaks down in non-Hermitian systems. In this paper, we reestablish the bulk-boundary correspondence in one-dimensional non-Hermitian systems by applying the scattering theory, which is a systematical way in various symmetry classes. Based on the scattering theory, it is discovered that the topological invariant can be obtained by solving a generalized eigenproblem without calculating the generalized Brillouin zone. As a direct consequence, we unveil a new type of topological phase transition without typical bulk enengy gap closing and an unstable …
The non-Hermitian but $\mathcal{PT}$-symmetric quantum field theories are known to have a pseudo-Hermitian interpretation. However the corresponding intertwining operator happens to be nonlocal that raises the question to what extent this nonlocality affects observable quantities. We consider the case when the intrinsic parity of the interaction terms is determined by degree of coupling constant. We show that the perturbative S-matrix of the equivalent Hermitian description can be easily obtained from the perturbative S-matrix of the non-Hermitian model. Namely, the first order vanishes wherea…
The descripition of in a Hermitian setting seemingly nonlocal and nonperturbative phenomena like confinement or superconductivity is most conveniently performed by generalizing quantum theory to a non-Hermitian regime where these phenomena appear perturbative and local. The short presentation provides a clue how this can be done on the basis of Lorentz covariance while preserving the analyticity of the theory. After deriving with the help of Lorentz covariance a quantum scalar product without making any use of metric or complex conjugation we sketch how the formalism of scattering theory can b…
The spectral singularity have been extensively studied over the last one and half decade for different non-Hermitian potentials in non-Hermitian quantum mechanics. The nature of spectral singularities have not been studied for the case of quaternionic potential. In the present work we perform an analytical study for the scattering from a quaternionic point interaction represented by delta function. New features of spectral singularities are observed which are different than the case of complex (non-quaternionic) point interaction. Most notable difference is the occurrence of spectral singulari…
Scattering States in One-Dimensional Non-Hermitian Baths
本文建立研究单个量子发射器耦合一维非厄米单能带浴散射态的通用方法，求解有限周期晶格散射态本征值方程，发现热力学极限下散射态非平面波叠加且局域化长度与晶格尺寸成比例，还给出Hatano-Nelson等浴的解析解。
The spectral singularity (SS) and coherent perfect absorption (CPA) have been extensively studied over the last one and half decade for different non-Hermitian potentials in non-Hermitian standard quantum mechanics (SQM) governed by Schrodinger equation. In the present work we explore these scattering features in the domain of non-Hermitian space fractional quantum mechanics (SFQM) governed by fractional Schrodinger equation which is characterized by Levy index $α$ ($ 1< α\leq 2$). We observe that non-Hermitian SFQM systems have more flexibility for SS and CPA and display some new features of …
Excited bound states are often understood within scattering based theories as resulting from the collision of a particle on a target via a short-range potential. We show that the resulting formalism is non-Hermitian and describe the Hilbert spaces and metric operator relevant to a correct formulation of such theories. The structure and tools employed are the same that have been introduced in current works dealing with PT-symmetric and quasi-Hermitian problems. The relevance of the non-Hermitian formulation to practical computations is assessed by introducing a non-Hermiticity index. We give a …
We highlight the conceptual issues that arise when one applies the quasi-Hermitian framework to analyze scattering from localized non-Hermitian potentials, in particular complex square-wells or delta-functions. When treated in the framework of conventional quantum mechanics, these potentials are generally considered as effective theories, in which probability is not conserved because of processes that have been ignored. However, if they are treated as fundamental theories, the Hilbert-space metric must be changed. In order for the newly-defined probability to be conserved, it must differ from …
Symmetry plays fundamental role in physics and the nature of symmetry changes in non-Hermitian physics. Here the symmetry-protected scattering in non-Hermitian linear systems is investigated by employing the discrete symmetries that classify the random matrices. The even-parity symmetries impose strict constraints on the scattering coefficients: the time-reversal (C and K) symmetries protect the symmetric transmission or reflection; the pseudo-Hermiticity (Q symmetry) or the inversion (P) symmetry protects the symmetric transmission and reflection. For the inversion-combined time-reversal symm…
The Hermitian systems possess unitary scattering; however, the Hermiticity is unnecessary for a unitary scattering although the scattering under the influence of non-Hermiticity is mostly non-unitary. Here we prove that the unitary scattering is protected by certain type of pseudo-Hermiticity and unaffected by the degree of non-Hermiticity. The energy conservation is violated in the scattering process and recovers after scattering. The subsystem of the pseudo-Hermitian scattering center including only the connection sites is Hermitian. These findings provide fundamental insights on the unitary…
Wave transport and scattering in open systems can be profoundly affected by non- Hermitian dynamics. In this work we consider wave scattering in a one-dimensional tight-binding lattice with a low-frequency harmonically-vibrating complex site potential. Floquet scattering is shown to be suppressed in a range of the spectral lattice band, which is limited by a singularity in the spectral transmission/reflection amplitudes for inelastic scattering channels. Invisibility over the entire spectral band is found when the singularity is pushed at the edge of the Brillouin zone, which requires a modula…
Dynamical Poles in Non-Hermitian Impurity Scattering
研究非厄米特杂质散射中动态极点对晚期时间信号的影响，揭示其与静态束缚态的区别及非厄米特格林函数分析结构的作用。
We analyze the scattering dynamics and spectrum of a quantum particle on a tight-binding lattice subject to a non-Hermitian (purely imaginary) local potential. The reflection, transmission and absorption coefficients are studied as a function of the strength of this absorbing potential. The system is found to have an exceptional point at a certain strength of the potential. Unusually, all (or nearly all) of the spectrum pairs up into mutually coalescing eigenstate pairs at this exceptional point. At large potential strengths, the absorption coefficient decreases and the effect of the imaginary…
Non-Hermitian optical scattering in cold atoms via four-wave mixing
提出利用相干多能级介质的非线性与两束相位失配驻波光束结合，在四能级双-Λ原子中实现完全可调谐的光学非互易多通道散射，为非厄米光学散射领域提供了新见解。
I review how methods from mesoscopic physics can be applied to describe the multiple wave scattering and complex wave dynamics in non-hermitian PT-symmetric resonators, where an absorbing region is coupled symmetrically to an amplifying region. Scattering theory serves as a convenient tool to classify the symmetries beyond the single-channel case and leads to effective descriptions which can be formulated in the energy domain (via Hamiltonians) and in the time domain (via time evolution operators). These models can then be used to identify the mesoscopic time and energy scales which govern the…
"Weak measurements" -- involving a weak unitary interaction between a quantum system and a meter followed by a projective measurement -- are investigated when the system has a non-Hermitian Hamiltonian. We show in particular how the standard definition of the "weak value" of an observable must be modified. These studies are undertaken in the context of bound state scattering theory, a non-Hermitian formalism for which the Hilbert spaces involved are unambiguously defined and the metric operators can be explicitly computed. Numerical examples are given for a model system.
We present an evaluation of some recent attempts at understanding the role of pseudo-Hermitian and PT-symmetric Hamiltonians in modeling unitary quantum systems and elaborate on a particular physical phenomenon whose discovery originated in the study of complex scattering potentials.
A flexible control of wave scattering in complex media is of relevance in different areas of classical and quantum physics. Recently, a great interest has been devoted to scattering engineering in non-Hermitian systems, with the prediction and demonstration of new classes of non-Hermitian potentials with unique scattering properties, such as transparent and invisibile potentials or one-way reflectionless potentials. Such potentials have been found for both continuous and discrete (lattice) systems. However, wave scattering in lattice systems displays some distinct features arising from the dis…
Non-Hermitian Gravitational Wave Scattering
本研究通过构建转移矩阵探讨引力波在谱奇点处的非厄米散射行为，发现地球观测的引力波频率与哈勃常数高度一致，为非厄米引力物理研究奠定基础。
A non-Hermitian interferometer can realize asymmetric transmission in the presence of imaginary potential and magnetic flux. Here, we propose a non-Hermitian dimer with an unequal hopping rate by an interferometer-like cluster in the framework of tight-binding model. The intriguing features of this design are the wave-vector independence and unidirectionality of scattering, which amplifies wavepacket without distortion and absorbs incoherent wave without reflection. The absorption relates to the system spectral singularities, the dynamical behaviors of the spectral singularities are also inves…
In quantum scattering, Hermiticity is necessary for both reciprocity and unitarity. Reciprocity means that both reflectivity (R) and transmitivity (T) are insensitive to the direction of incidence of a wave (particle) at a scatterer from left/right. Unitarity means that R+T=1. In scattering from non-Hermitian PT-symmetric structures the (left/right) handedness (non-reciprocity) of reflectivity is known to be essential and unitarity remains elusive so far. Here we present a surprising occurrence of both reciprocity and unitarity in scattering from a complex PT-symmetric potential. In special ca…
Particle beam scattering is a conventional technique for detecting the nature of matter. We studied the scattering problem of a cluster connected to multiple leads. We established the connection between the eigenstate of the topological scattering center and the transmission and reflection amplitudes for the resonant scattering process. We discovered that as an application, this approach enables the detection of the edge state in the band gap for both Hermitian and non-Hermitian systems and the identification of the topology of a system. We investigated two types of Su-Schrieffer-Heeger chains…
In non-Hermitian scattering problems the behavior of the transmission probability is very different from its Hermitian counterpart; it can exceed unity or even be divergent, since the non-Hermiticity can add or remove the probability to and from the scattering system. In the present paper, we consider the scattering problem of a PT-symmetric potential and find a counter-intuitive behavior. In the usual PT-symmetric non-Hermitian system, we would typically find stationary semi-Hermitian dynamics in a regime of weak non-Hermiticity but observe instability once the non-Hermiticity goes beyond an …
Exploring Metamaterial Lasers through Non-Hermitian Scattering Formalism
本研究通过非厄米散射形式理论分析光在负折射率超材料中的行为，建立传输矩阵并确定频谱奇异性条件，为超材料平板激光器和相干完美吸收器系统的参数微调提供理论基础。
We present a generalization of the perturbative construction of the metric operator for non-Hermitian Hamiltonians with more than one perturbation parameter. We use this method to study the non-Hermitian scattering Hamiltonian: H=p^2/2m+ζ_-δ(x+a)+ζ_+δ(x-a), where ζ_\pm and a are respectively complex and real parameters and δ(x) is the Dirac delta function. For regions in the space of coupling constants ζ_\pm where H is quasi-Hermitian and there are no complex bound states or spectral singularities, we construct a (positive-definite) metric operator ηand the corresponding equivalent Hermitian H…
One of the simplest non-Hermitian Hamiltonians first proposed by Schwartz (1960 {\it Commun. Pure Appl. Math.} \tb{13} 609) which may possess a spectral singularity is analyzed from the point of view of non-Hermitian generalization of quantum mechanics. It is shown that $η$ operator, being a second order differential operator, has supersymmetric structure. Asymptotic behavior of eigenfunctions of a Hermitian Hamiltonian equivalent to the given non-Hermitian one is found. As a result the corresponding scattering matrix and cross section are given explicitly. It is demonstrated that the possible…
Unlike a Chern number in $2$D and $3$D topological system, Zak phase takes a subtle role to characterize the topological phase in $1$D. On the one hand, it is not a gauge invariant, on the other hand, the Zak phase difference between two quantum phases can be used to identify the topological phase transitions. A non-Hermitian system may inherit some characters of a Hermitian system, such as entirely real spectrum, unitary evolution, topological energy band, etc. In this paper, we study the influence of non-Hermitian term on the Zak phase for a class of non-Hermitian systems. We show exactly th…
Lévy-index control of spectral singularities and coherent perfect absorption in non-Hermitian space-fractional quantum mechanics
本研究通过调节莱维指数α，探索非本征空间分数量子力学中谱奇点和相干完美吸收的控制机制，揭示了分数量子动力学对非本征散射的影响。
The study of a particle with position-dependent effective mass (pdem), within a double heterojunction is extended into the complex domain --- when the region within the heterojunctions is described by a non Hermitian ${\cal{PT}}$ symmetric potential. After obtaining the exact analytical solutions, the reflection and transmission coefficients are calculated, and plotted as a function of the energy. It is observed that at least two of the characteristic features of non Hermitian ${\cal{PT}}$ symmetric systems --- viz., left / right asymmetry and anomalous behaviour at spectral singularity, are p…
Pseudo-Hermiticity protects the energy-difference conservation in the scattering
本研究发现非厄米散射系统中由赝厄米性保护的能量差守恒律，通过两个典型反PT对称系统验证了该守恒律的成立与失效，为非厄米系统的相关物理研究提供了新见解。
Maxwell demon no-go theorem for multichannel scattering
本文针对多通道散射系统提出麦克斯韦妖不可行定理，证明无论哈密顿量多复杂都无法通过单一渐近通道逼近妖行为，并引入参数量化距离，提出在量子光学装置中构建最接近妖行为设备的方法。
While classic quantum chaos originated from the idea to set into context nonlinear physics and Hermitian quantum mechanics, non-Hermitian models have enhanced the field in recent years. At the same time, low-dimensional effective matrix models have proven to be a powerful tool in accessing the physical properties of a system in a semiquantitative manner. Here, we focus on two realizations of non-Hermitian physics in mesoscopic systems. First, we consider spiral optical microcavities in which the asymmetric scattering between whispering gallery modes induces the non-Hermitian behaviour. Second,…
We examine the notion and properties of the non-Hermitian effective Hamiltonian of an unstable system using as an example potential resonance scattering with a fixed angular momentum. We present a consistent self-adjoint formulation of the problem of scattering on a finite-range potential, which is based on separation of the configuration space on two, internal and external, segments. The scattering amplitude is expressed in terms of the resolvent of a non-Hermitian operator H. The explicit form of this operator depends both on the radius of separation and the boundary conditions at this place…
Scattering of TE and TM waves and quantum dynamics generated by non-Hermitian Hamiltonians
本研究将平面对称线性介质的电磁波散射简化为TE/TM模问题，通过动力学表述把转移矩阵技术拓展到非均匀介质，将散射求解转化为Riccati方程初值问题，并应用于无反射介质的识别。
We formulate a new quasi-Hermitian delta-shell pseudopotential for higher partial wave scattering, and show that any such potential must have an energy-dependent regularization. The quasi-Hermiticity of the Hamiltonian leads to a complete set of biorthogonal wave functions that can be used as a basis to expand and diagonalize other two-body Hamiltonians. We demonstrate this procedure for the case of ultracold atoms in a polarization-gradient optical lattice, interacting pairwise when two atoms are transported together from separated lattice sites. Here the pseudopotential depends explicitly on…
Exact joint eigenvalue densities of non-Hermitian random matrices are Calogero scattering states
该研究解决了任意规模下具有转置对称性的非厄米随机矩阵的精确联合本征值密度问题，将其与Calogero模型的散射态关联，还计算了复能级间距分布和两点谱关联函数，揭示了随机矩阵、可积性与对称性的相互作用。
We study the effect of PT-symmetric complex potentials on the transport properties of non-Hermitian systems, which consist of an infinite linear chain and two side-coupled defect points with PT-symmetric complex on-site potentials. By analytically solving the scattering problem of two typical models, which display standard Fano resonances in the absence of non-Hermitian terms, we find that the PT-symmetric imaginary potentials can lead to some pronounced effects on transport properties of our systems, including changes from the perfect reflection to perfect transmission, and rich behaviors for…
We theoretically study the non-Hermitian systems, the non-Hermiticity of which arises from the unequal hopping amplitude (UHA) dimers. The distinguishing features of these models are that they have full real spectra if all of the eigenvectors are time-reversal (T) symmetric rather than parity-time-reversal (PT) symmetric, and that their Hermitian counterparts are shown to be an experimentally accessible system, which have the same topological structures as that of the original ones but modulated hopping amplitudes within the unbroken region. Under the reflectionless transmission condition, the…
Superuniversal Statistics of Complex Time-Delays in Non-Hermitian Scattering Systems
本文通过微波实验测量一维图、二维台球和三维腔体的多端口S矩阵，计算复Wigner-Smith及反射、透射时间延迟，发现各时间延迟量实部和虚部分布的大延迟尾部具有与维度、通道数、对称类和衰减无关的超普适统计，并将其与散射奇点的拓扑性质联系起来。
Fundamental Limits of Non-Hermitian Sensing from Quantum Fisher Information
通过散射矩阵形式分析非厄米系统中的量子Fisher信息，证明奇异点可增强传感性能，且远离奇异点可进一步提高灵敏度。
In the Feshbach projection operator (FPO) formalism the whole function space is divided into two subspaces. One of them contains the wave functions localized in a certain finite region while the continuum of extended scattering wave functions is involved in the other subspace. The Hamilton operator of the whole system is Hermitian, that of the localized part is, however, non-Hermitian. This non-Hermitian Hamilton operator $H_{\rm eff}$ represents the core of the FPO method in present-day studies. It gives a unified description of discrete and resonance states. Furthermore, it contains the time…
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