C. Yuce
A condition to have a real spectrum for a non-Hermitian Hamiltonian is given. As special cases, it is shown that the condition is reduced to Hermiticity and PT symmetric conditions.
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Metric Operators for Quasi-Hermitian Hamiltonians and Symmetries of Equivalent Hermitian Hamiltonians
我们给出了一个简单的证明的事实，即每一个可对角化的运营商，有一个真正的频谱是准厄米特和显示如何度量运营商与准厄米特哈密顿相关的对称发电机的等效厄米特哈密顿。
Non-Hermitian PT-symmetric and Hermitian Hamiltonians' correspondence: Isospectrality and mass signature
变换的形式x到iy; x，y在R中，或一个等价的相似变换与度量算子$η$的非厄米PT对称哈密顿变换成厄米伙伴哈密顿在希尔伯特空间。等谱和质量签名进行了讨论。
A new class of non-Hermitian Hamiltonians with real spectra
构造了一类新的具有实谱的非厄米哈密顿算子。哈密顿算符有一个明确已知的本征函数。
An algorithm for finding the bound-state eigenvalues and eigenfunctions of a Hermitian Hamiltonian operator using Green's method, developed by Waxman\cite{W98},has been extended to include non-Hermitian Hamiltonian operators.
Pseudo-Hermitian versus Hermitian position-dependent-mass Hamiltonians in a perturbative framework
我们制定了一个系统的算法，用于构建一类厄米位置相关的质量哈密顿量，最低阶的微扰理论，允许PT对称哈密顿量的描述。该方法适用于厄米模拟的PT对称立方非谐振子。一个新的例子是提供了一个哈密顿（近似）相当于一个PT对称的扩展的单参数三角Poschl-Teller势。
Non-Hermitian von Roos Hamiltonian's $η$-weak-pseudo-Hermiticity, isospectrality and exact solvability
考虑了复化的von Roos哈密顿量，并利用厄米一阶纠缠微分算子得到了相应的位置依赖质量$η$ -弱赝厄米哈密顿量.利用Liouville型变量变换，将$η$ -弱伪埃尔米特von Roos哈密顿量H（x）映射到传统的Schrodinger哈密顿量形式H（q），得到了H（x）和H（q）之间的精确等谱对应.在用户友好的位置相关质量设置下，观察到对于每个精确可解的$η$ -弱伪厄米特参考-哈密顿量H（q），存在一组精确可解的$η$ -弱伪厄米特等谱目标-哈密顿量H（x）。以非厄米PT对称Scarf II势和非厄米π型PT对称Samsonov-Roy势为参考模型，得到了相应的$η$ -弱伪厄米等谱目标哈密顿量.
On Pseudo-Hermitian Hamiltonians
本文研究了伪厄米哈密顿量的$η$算子的构造问题。我们给出了一个充分条件，可以利用它来系统地产生一个序列的$η$运营商从一个已知的，从而证明了非唯一性的$η$的一个特定的伪厄米哈密顿。我们还研究了扰动哈密顿量，其中$η$的对应于原来的哈密顿量仍然工作。
On Finite $J$-Hermitian Quantum Mechanics
在最近的论文arXiv：1312.7738中，作者讨论了$J$ -厄米量子力学，并证明了$PT$ -对称量子力学本质上是$J$ -厄米量子力学.本文讨论了由连续统力学自然导出的有限$J$ -厄米量子力学及其与有限$PT$ -对称量子力学的关系。
A physical interpretation for the non-Hermitian Hamiltonian
我们探索一种方法，找到一个非厄米哈密顿和厄米之间的联系。本文在分析一类非厄米哈密顿量的Bethe Anasterian解和相应的厄米哈密顿量的散射问题的基础上，结果表明，以链为散射中心的任意厄米特晶格的散射态与相应的非厄米特紧束缚晶格（由厄米特晶格加上两个在位复势构成）具有相同的波函数，无论非厄米特晶格是破缺PT对称还是非PT对称.最后给出了一个可精确求解的模型来说明本文的主要观点。
In this work we address systems described by time-dependent non-Hermitian Hamiltonians under time-dependent Dyson maps. We shown that when starting from a given time-dependent non-Hermitian Hamiltonian which is not itself an observable, an infinite chain of gauge linked time-dependent non-observable non-Hermitian Hamiltonians can be derived from it. The matrix elements of the observables associated with all these non observable Hamiltonians are, however, all linked to each other, and in the particular case where global gauges exist, these matrix elements becomes all identical to each other. In…
P,T,PT, and CPT invariance of Hermitian Hamiltonians
目前，已经声称某些厄米哈密顿量具有宇称（P），并且它们是PT不变的。我们提出了广义的时间反演算子（T）和标准正交性的定义，使得所有的厄米哈密顿量是P，T，PT和CPT不变。PT-范数和CPT-范数分别是不定的和确定的。能量本征态是E型（例如，偶数）或O型（例如，奇数）。C模拟电荷共轭对称，这是最近发现存在的非厄米哈密顿。对于厄米哈密顿量，它与P重合。
We generalize a recently proposed approach for the construction of pseudo-Hermitian Hamiltonians with real spectra. Present technique is based on a simple and straightforward similarity transformation of the coordinate and momentum.
We discuss Hamiltonian symmetries and invariants for quantum systems driven by non-Hermitian Hamiltonians. For time-independent Hermitian Hamiltonians, a unitary or antiunitary transformation $AHA^\dagger$ that leaves the Hamiltonian $H$ unchanged represents a symmetry of the Hamiltonian, which implies the commutativity $[H,A]=0$, and a conservation law, namely the invariance of expectation values of $A$. For non-Hermitian Hamiltonians, $H^\dagger$ comes into play as a distinct operator that complements $H$ in generalized unitarity relations. The above description of symmetries has to be exten…
On a class of non-Hermitian Hamiltonians with tridiagonal matrix representation
本研究探讨一类三对角矩阵形式的非厄米哈密顿量，证明其可通过厄米正定对角算符实现准厄米性或与厄米算符相似，揭示开放与周期边界条件的关键差异，并用两个常用简单模型验证理论。
Spectral singularities of non-Hermitian Hamiltonians and SUSY transformations
给出了在$L^2(R^+)$中定义的具有纯实谱的非厄米哈密顿量的简单例子，这些哈密顿量在连续谱内具有谱奇异性。它表明，这样的哈密顿可能会出现通过移动到复平面的实势的n因变量。它们也可以被创造为厄米特哈密尔顿的超对称伙伴。在后一种情况下，非厄米哈密顿量的谱奇点是其厄米超对称伙伴的连续谱的寻常点。当一个具有复本征能和谱奇异性的复势有一个具有无谱奇异性的实谱的超对称性伙伴时，给出了变换函数的条件。最后，我们简短地讨论为什么哈密顿谱奇点是“坏”。
We study the time evolution of quantum systems with a time-dependent non-Hermitian Hamiltonian given by a linear combination of SU(1,1) and SU(2) generators.With a time-dependent metric, the pseudo-Hermitian invariant operator is constructed in the same manner as for both the SU(1,1) and SU(2) systems. The exact common solutions of the Schrödinger equations for both the SU(1,1) and SU(2) systems are obtained in terms of eigenstates of the pseudo-Hermitian invariant operator.
The formalism for non-Hermitian quantum systems sometimes blurs the underlying physics. We present a systematic study of the vielbein-like formalism which transforms the Hilbert space bundles of non-Hermitian systems into the conventional ones, rendering the induced Hamiltonian to be Hermitian. In other words, any non-Hermitian Hamiltonian can be "transformed" into a Hermitian one without altering the physics. Thus we show how to find a reference frame (corresponding to Einstein's quantum elevator) in which a non-Hermitian system, equipped with a non-trivial Hilbert space metric, reduces to a …
We generalize a recently proposed algebraic method in order to treat non-Hermitian Hamiltonians. The approach is applied to several quadratic Hamiltonians studied earlier by other authors. Instead of solving the Schrödinger equation we simply obtain the eigenvalues of a suitable matrix representation of the operator. We take into account the existence of unitary and antiunitary symmetries in the quantum-mechanical problem.
We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an ac…
Supersymmetric solutions of PT-/non-PT-symmetric and non-Hermitian Screened Coulomb potential via Hamiltonian hierarchy inspired variational method
通过求解指数余弦屏蔽库仑势的薛定谔方程，得到了PT对称和厄米/非厄米形式量子系统的超对称解.利用哈密顿体系启发的变分方法得到了近似的能量本征值和相应的波函数。
We consider the description of open quantum systems with probability sinks (or sources) in terms of general non-Hermitian Hamiltonians.~Within such a framework, we study novel possible definitions of the quantum linear entropy as an indicator of the flow of information during the dynamics. Such linear entropy functionals are necessary in the case of a partially Wigner-transformed non-Hermitian Hamiltonian (which is typically useful within a mixed quantum-classical representation). Both the case of a system represented by a pure non-Hermitian Hamiltonian as well as that of the case of non-Hermi…
A class of spherically-separable non-Hermitian PphiTphi-symmetric Hamiltonians
研究了一类球型非厄米特势。证明了相应的非厄米哈密顿量具有“新的”P $phi$ T $phi$ -对称性.我们观察到，虽然这样的P $phi$ T $phi$ -对称哈密顿量只是复制了V（r）的本征值，但由于方位角部分的变化，相应的波函数将更倾向于包含一些新的概率解释。
Here we present an strategy for the derivation of a time-dependent Dyson map which ensures simultaneously the unitarity of the time evolution and the observability of a quasi-Hermitian Hamiltonian. The time-dependent Dyson map is derived through a constructed Schrödinger-like equation governed by the non-Hermitian Hamiltonian itself; despite its time-dependence our scheme ensures the time-independence of the metric operator, a necessary condition for the observability of the quasi-Hermitian Hamiltonian. As an illustrative example we consider a driven Harmonic oscillator described by a time-dep…
In contrast to classical systems, actual implementation of non-Hermitian Hamiltonian dynamics for quantum systems is a challenge because the processes of energy gain and dissipation are based on the underlying Hermitian system-environment dynamics that is trace preserving. Recently, a scheme for engineering non-Hermitian Hamiltonians as a result of repetitive measurements on an anicillary qubit has been proposed. The induced conditional dynamics of the main system is described by the effective non-Hermitian Hamiltonian arisng from the procedure. In this paper we demonstrate the effectiveness o…
Adiabaticity condition for non-Hermitian Hamiltonians
我们推广人口的概念，非厄米特系统在不同的方式，并确定一个最适合的特点绝热性。本文还提出了一个与此选择相一致的近似绝热准则。例子提供了不同的过程，涉及两个级别的原子衰变。
Non-Hermitian SUSY Hydrogen-like Hamiltonians with real spectra
证明了氢哈密顿量的径向部分可分解为两个互不共轭的一阶微分算子加一个复常数的乘积。1-susy方法被用来构建非厄米哈密顿与氢光谱。其他非埃尔米特汉密尔顿被证明承认在ε处有额外的“复能量”。利用复共轭对的2-susy变换，导出了新的自伴类氢哈密顿量.
The non-Hermitian Schrödinger equation is re-expressed generally in the form of Hamilton's canonical equation without any approximation. Its quantization called non-Hermitian quantum field theory is discussed. By virtue of the canonical equation, the theory of non-Hermitian quantum mechanics is totally reformulated, including the probability amplitudes of states, the expectations of operators, as well as the expressions of interaction terms. The conventional difficulties in non-Hermitian quantum mechanics are totally overcome by the reformulation. Specifically, the imaginary parts the non-Herm…
We provide the first solution of a time-dependent metric operator for the non-Hermitian Jaynes-Cummings Hamiltonian. We use this solution to calculate the entanglement between two identical isolated such Hamiltonians. The presence of a non-Hermitian interaction term leads to a spontaneously broken $\mathcal{PT}$-symmetric regime which manifests itself in the exotic time-evolution of entanglement. When the symmetry is broken, oscillatory modes transition into decay. As such that there is a drastic difference in behaviour between the broken and unbroken regimes.
Pseudo-Hermitian Hamiltonians, indefinite inner product spaces and their symmetries
本文将广义宇称$P$、电荷共轭$C$和时间反演$T$算子的定义推广到不可对角化的伪厄米哈密顿算子，并根据四重分类用这些广义算子描述伪厄米哈密顿算子的全部对称性.特别地，我们证明了$TP$和$CTP$是反酉对称的生成元，并且给出了伪厄米哈密顿$H$允许$P$ -反射对称生成$P$ -伪酉和$P$ -伪反酉对称的充要条件.最后，给出了一个物理实例，并对物理系统的$P$ -幺正演化给出了一些启示。
Matrix Algebras in Non-Hermitian Quantum Mechanics
原则上，非厄米量子运动方程可以用海森堡或薛定谔的量子动力学图像作为起点来表述。在这里，它显示在这两种情况下，如何映射的代数的代数算子，定义的时间演化方面的一个非厄米特哈密顿，到一个非哈密顿代数与厄米特哈密顿。这种推导背后的逻辑是可逆的，因此任何厄米特哈密顿算子都可以通过一个合适的广义（非哈密顿）代数来用于非厄米特动力学的公式化。这些结果为开放量子系统动力学的计算机模拟提供了非厄米运动方程的一般结构（模板）。
We investigate in this paper time-dependent non-Hermitian Hamiltonians, which consist respectively of SU(1,1) and SU(2) generators. The former Hamiltonian is PT symmetric but the latter one is not. A time-dependent non-unitary operator is proposed to construct the non-Hermitian invariant, which is verified as pseudo-Hermitian with real eigenvalues. The exact solutions are obtained in terms of the eigenstates of the pseudo-Hermitian invariant operator for both the SU(1,1)and SU(2)systems in a unified manner. Then, we derive the LR phase, which can be separated to the dynamic phase and the geome…
On the pseudo-Hermitian nondiagonalizable Hamiltonians
考虑一类具有离散谱的（可能不可对角化的）伪厄米特算子，证明了在任何情况下（除非它们是可对角化的并且具有实谱）它们都不是关于半定内积的厄米特算子，并且伪厄米特性质等价于反线性对合对称的存在.此外，我们表明，一个典型的退化的实本征值（这减少到众所周知的克雷默退化的埃尔米特的情况下）发生时，费米子（可能nondiagonalizable）伪埃尔米特哈密顿承认一个反线性对称的时间反演算子$T$。一些后果和应用进行了简要讨论。
The Pure State Space of Quantum Mechanics as Hermitian Symmetric Space
研究了量子力学的纯态空间作为Hermite对称Kaehler流形。在这种非线性几何背景下讨论了量子力学的经典原理（量子叠加原理、海森堡不确定原理、量子概率原理）和观测量的谱理论。
On Pseudo-Hermitian Hamiltonians and Their Hermitian Counterparts
在量子力学中两个特别有趣的非厄米模型的背景下，我们探讨了原始哈密顿量H和厄米对应物H之间的关系，H通过相似变换从H获得，正如Mostafazadeh所指出的那样。在第一个模型中，由于斯旺森，h原来只是一个标度谐振子，这解释了它的频谱的形式。然而，变换不是唯一的，这也意味着原始理论的可观测量不是由H单独唯一确定的。我们考虑的第二个模型是原始的PT不变哈密顿量，势为V= igx ^[3]。在这种情况下，我们只能在微扰论中构造的相应的h对应于一个复杂的速度依赖势。我们再次探讨了正则变量x和p与可观测量X和P之间的关系。
On the eigenvalues of some non-Hermitian Hamiltonians with space-time symmetry
本文利用伪谱方法和在适当的基组上对哈密顿矩阵直接对角化的方法，计算了一些二维非厄米哈密顿算子的特征值。这两套结果同意非常好，但有很大的不同，从本征值前一段时间由其他作者。特别是，我们没有观察到多个相变声称发生在一个非谐振子。
Reply to Comment on "Non Hermitian Quantum Mechanics with Minimal Length Uncertainty", arXiv:0908.2341
结果表明，文献[1]的结果是一致的。
Time-dependent quasi-Hermitian Hamiltonians and the unitarity of quantum evolution
我们证明了在伪厄米哈密顿量H=H（t）中引入明显的时间依赖性的后果远没有A. Mostafazadeh in Phys. Lett. B 650（2007）208（arXiv：0706.1872v2 [quant-ph]）。特别地，演化的酉性不需要度量$η_+=η_+(t)$的时间无关性。
All Hermitian Hamiltonians Have Parity
证明了：如果一个哈密顿量$H$是厄米算符，则总存在一个具有下列性质的算子P：（i）P是线性厄米算符;（ii）P与H交换;（iii）P^2=1;（iv）H的第n个本征态也是P的本征态，其本征值为（-1）^n.鉴于这些性质，将P称为宇称算子并说H具有宇称对称性是合适的，即使P可能不是指空间反射。因此，如果哈密顿量具有H=p^2+V（x）的形式，其中V（x）是实数（因此H具有时间反演对称性），那么它立即得出H具有PT对称性。这表明PT对称性是厄米性的推广：所有形式为H=p^2+V（x）的厄米哈密顿量都具有PT对称性，但并非所有这种形式的PT对称哈密顿量都是厄米的。
It has been argued that it is incompatible to maintain unitary time-evolution for time-dependent non-Hermitian Hamiltonians when the metric operator is explicitly time-dependent. We demonstrate here that the time-dependent Dyson equation and the time-dependent quasi-Hermiticity relation can be solved consistently in such a scenario for a time-dependent Dyson map and time-dependent metric operator, respectively. These solutions are obtained at the cost of rendering the non-Hermitian Hamiltonian to be a non-observable operator as it ceases to be quasi-Hermitian when the metric becomes time-depen…
We study the connection between a family of non-Hermitian Hamiltonians H and Hermitian ones H based on exact solutions. In general, for a dynamic process in a non-Hermitian system H, there always exists a parallel dynamic process governed by the corresponding Hermitian conjugate Hamiltonian H†. We show that a linear superposition of the two parallel dynamics is exactly equivalent to the time evolution of a state under a Hermitian Hamiltonian H. It reveals a novel connection between non-Hermitian and Hermitian systems.
The counterpart of the rotating wave approximation for non-Hermitian Hamiltonians is considered, which allows for the derivation of a suitable effective Hamiltonian for systems with some states undergoing decays. In the limit of very high decay rates, on the basis of this effective description we can predict the occurrence of a quantum Zeno dynamics which is interpreted as the removal of some coupling terms and the vanishing of an operatorial pseudo-Lamb shift.
The breakdown of Ehrenfest's theorem imposes serious limitations on quaternionic quantum mechanics (QQM). In order to determine the conditions in which the theorem is valid, we examined the conservation of the probability density, the expectation value and the classical limit for a non-anti-hermitian formulation of QQM. The results also indicated that the non-anti-hermitian quaternionic theory is related to non-hermitian quantum mechanics, and thus the physical problems described with both of the theories should be related.
Non-Hermitian Quantum Mechanics with Minimal Length Uncertainty
我们研究存在极小长度的非厄米量子力学。特别地，我们得到了非厄米位移谐振子和具有最小长度不确定性的Swanson模型的精确解。在这两种情况下的频谱被发现是真实的。它也表明，该模型是$η$伪厄米特和度量运营商被发现明确在这两种情况下。
We in this paper demonstrate that the $PT$-symmetric non-Hermitian Hamiltonian for a periodically driven system can be generated from a kernel Hamiltonian by a generalized gauge transformation. The kernel Hamiltonian is Hermitian and static, while the time-dependent transformation operator has to be $PT$ symmetric and non-unitary in general. Biorthogonal sets of eigenstates appear necessarily as a consequence of non-Hermitian Hamiltonian. We obtain analytically the wave functions and associated non-adiabatic Berry phase $γ_{n}$ for the $n$th eigenstate. The classical version of the non-Hermiti…
Spherical-separablility of non-Hermitian Dirac Hamiltonians and pseudo-PT-symmetry
考虑了一个非厄米P $_ϕ$ T $_ϕ$对称化的球可分Dirac哈密顿量.可以观察到，后代哈密顿算子H $_{r}$、H $_θ$和H $_ϕ$起着重要的作用，并提供了一些用户自由的选择，以确定它们中的哪一个（或哪些）是非厄米特的。考虑P $_ϕ$ T $_ϕ$对称H $_ϕ$，我们证明了传统的相对论能量本征值是可恢复的.我们还看到了一般波函数方位角部分不可避免的变化。此外，在后代哈密顿量H $_θ$中设置可能的相互作用$V(θ)$ =0也将表明通解的角度$θ$相关部分的变化。虽然一些P $_ϕ$ T $_ϕ$ -对称化H $_ϕ$哈密顿被认为是，一个配方，以保持常规的磁量子数m，定义在常规的传统厄米设置，建议。哈密顿具有类似于PT对称的性质（这里是非厄米特的
Non-Hermitian Hamiltonians with real eigenvalues coupled to electric fields: from the time-independent to the time dependent quantum mechanical formulation
我们提供了一个回顾式介绍量子力学形式主义与非厄米哈密顿系统的实本征值。从时间无关的框架，我们解释了如何确定一个适当的域的非厄米哈密顿量，并特别注意PT对称性和伪厄米性所发挥的作用。我们讨论了这种系统的时间演化，特别是考虑到如何始终耦合的电场伪厄米哈密顿的问题。我们用三个明确的例子来说明一般形式：i）广义斯旺森哈密顿量，它构成了非谐振子的非厄米延拓; ii）尖峰谐振子，它表现出明确的超对称性; iii）-x^4-势，它是量子场论的一个玩具模型。
Parity-time (PT) symmetric non-Hermitian Hamiltonians bring about many novel features and interesting applications such as quantum gates faster than those in Hermitian systems, and topological state transfer. The performance of evolutions under $\mathcal{PT}$-symmetric Hamiltonians is degraded by the inevitable noise and errors due to system-environment interaction and experimental imperfections. In contrast to Hermitian Hamiltonians, the fluctuations in dissipative beams that are utilized to generate non-Hermitian contributions in the PT-symmetric Hamiltonians cause additional errors. Here we…
Energy-dependent Hamiltonians and their pseudo-Hermitian interpretation
重新分析了量子力学中的能量相关力概念。我们建议简化他们的研究，通过表示每个自伴和能量相关的哈密顿量H=H（E）与实谱的一个辅助的非厄米算子K，保持能量无关。这种方法的实用价值的薛定谔方程与能量相关的潜力说明使用其准精确可解的例子。
Exponential Type Complex and non-Hermitian Potentials in PT-Symmetric Quantum Mechanics and Hamiltonian Hierarchy Method
通过求解薛定谔方程，得到了PT-/非PT-对称非厄米变形Morse势和Pöschl-Teller势的超对称解.利用Hamilton族方法得到了系统的实能量本征值和相应的本征函数。\newline {PACS：05.20.- 05：30- d; 05.70。Ce; 03.65. w} \newline { \it Keywords}{ \small：超对称量子力学，Hamiltonian Hierarchy Method，Morse potential，Pöschl-Teller potential}
A New Class of Adiabatic Cyclic States and Geometric Phases for Non-Hermitian Hamiltonians
对于T-周期非厄米哈密顿量H（t），构造了一类周期为T的绝热循环态，它们不是初始哈密顿量H（0）的本征态.我们证明了相应的绝热几何相位角是实的，并讨论了它们与传统的复绝热几何相位角的关系。本文详细计算了旋进磁场中自旋为1/2的非厄米粒子的新绝热循环态及其几何相位。
We show that similarity (or equivalent) transformations enable one to construct non-Hermitian operators with real spectrum. In this way we can also prove and generalize the results obtained by other authors by means of a gauge-like transformation and its generalization. Such similarity transformations also reveal the connection with pseudo-Hermiticity in a simple and straightforward way. In addition to it we consider the positive and negative eigenvalues of a three-parameter non-Hermitian oscillator.
Determining non-Hermitian parent Hamiltonian from a single eigenstate
针对非厄米系统哈密顿量确定通常需左右本征态对的问题，提出基于量子协方差矩阵、利用单个左/右本征态求解复零向量来确定非厄米哈密顿量的方法，经数值验证具稳定性，适配实验量子系统仅能获取右本征态的场景。
On the η pseudo PT symmetry theory for non-Hermitian Hamiltonians: time-dependent systems
本文针对含时非厄米哈密顿量，提出一种新度量η(t)=PTη(t)以同时推导伪PT对称性与η伪厄米性，求解SU(1,1)模型并给出物理应用。
Non Hermitian Operators with Real Spectrum in Quantum Mechanics
例子给出的非厄米哈密顿算子，有一个真正的频谱。一些调查运营商表示的Weil-Heisenberg代数的生成元。有人认为，存在一个对合运营商$\hat J$，使汉密尔顿$\hat J$ -厄米导致明确的定义相关的正定规范允许标准的概率解释的量子力学。Poeschl-Teller哈密顿量的非厄米扩展也被考虑。构造了由相似变换得到的厄米特对应体。
An optimum Hamiltonian for non-Hermitian quantum evolution and the complex Bloch sphere
对于一个由非厄米哈密顿量控制的量子系统，我们研究了在最小时间$τ$内获得一个最佳哈密顿量的问题，该最佳哈密顿量能使给定的初始态到某个最终态的非幺正变换.该分析是基于希尔伯特空间的初始和最终状态和二维复布洛赫球的点所跨越的二维子空间的状态之间的关系。
Non-Hermitian d-dimensional Hamiltonians with position dependent mass and their $η$-pseudo-Hermiticity generators
提出了一类具有位置相关质量的非厄米d维Hamilton系统及其$η$ -伪厄米性生成元.针对不同的位置相关质量设置，在1D、2D和3D中给出了说明性示例。
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…
We introduce and study a class of non-Hermitian Hamiltonians which have velocity dependent potentials. Since stability can not be advocated directly from the classical potential, we show that the energy spectra are real and bounded from below which proves the stability of the spectra of all members in the class. We find that the introduced class of non-Hermitian Hamiltonians do have a corresponding superpartner class of non-Hermitian Hamiltonians. We were able to introduce supercharges which in conjunction with the corresponding super Hamiltonians constitute a closed super algebra. Among the i…
Non-Hermitian Hamiltonians with a Real Spectrum and Their Physical Applications
我们提出了一个评估的一些最近的尝试，在理解的作用，伪厄米和PT-对称哈密顿在建模单一的量子系统，并阐述了一个特定的物理现象，其发现起源于复杂的散射势的研究。
We propose a scheme to deal with certain time-dependent non-Hermitian Hamiltonian operators $H(t)$ that generate a real phase in their time-evolution. This involves the use of invariant operators $I_{PH}(t)$ that are pseudo-Hermitian with respect to the time-dependent metric operator, which implies that the dynamics is governed by unitary time evolution. Furthermore, $H(t)$ is not generally quasi-Hermitian and does not define an observable of the system but $I_{PH}(t)$ obeys a quasi-hermiticity transformation as in the completely time-independent Hamiltonian systems case. The harmonic oscillat…
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