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Journal articles on the topic 'Non-Hermitian Hamiltonian'

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Published: 6 September 2023
Last updated: 31 July 2025

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1

Yeşiltaş, Özlem. "Non-Hermitian Dirac Hamiltonian in Three-Dimensional Gravity and Pseudosupersymmetry." Advances in High Energy Physics 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/484151.

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The Dirac Hamiltonian in the(2+1)-dimensional curved space-time has been studied with a metric for an expanding de Sitter space-time which is two spheres. The spectrum and the exact solutions of the time dependent non-Hermitian and angle dependent Hamiltonians are obtained in terms of the Jacobi and Romanovski polynomials. Hermitian equivalent of the Hamiltonian obtained from the Dirac equation is discussed in the frame of pseudo-Hermiticity. Furthermore, pseudosupersymmetric quantum mechanical techniques are expanded to a curved Dirac Hamiltonian and a partner curved Dirac Hamiltonian is gene
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2

Samsonov, Boris F. "Hermitian Hamiltonian equivalent to a given non-Hermitian one: manifestation of spectral singularity." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1989 (2013): 20120044. http://dx.doi.org/10.1098/rsta.2012.0044.

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One of the simplest non-Hermitian Hamiltonians, first proposed by Schwartz in 1960, that may possess a spectral singularity is analysed from the point of view of the non-Hermitian generalization of quantum mechanics. It is shown that the η operator, being a second-order differential operator, has supersymmetric structure. Asymptotic behaviour of the 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 presence of a spectral singu
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3

Grimaudo, Roberto, Antonino Messina, Alessandro Sergi, Nikolay V. Vitanov, and Sergey N. Filippov. "Two-Qubit Entanglement Generation through Non-Hermitian Hamiltonians Induced by Repeated Measurements on an Ancilla." Entropy 22, no. 10 (2020): 1184. http://dx.doi.org/10.3390/e22101184.

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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, which are trace preserving. Recently, a scheme for engineering non-Hermitian Hamiltonians as a result of repetitive measurements on an ancillary qubit has been proposed. The induced conditional dynamics of the main system is described by the effective non-Hermitian Hamiltonian arising from the procedure. In this paper, we demonstrate the effectivene
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4

Sharma, Preet. "𝒫𝒯-Symmetric Quantum Mechanics Basics & Zeeman Effect". Reports in Advances of Physical Sciences 04, № 03 (2020): 2050006. http://dx.doi.org/10.1142/s2424942420500061.

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The non-Hermitian aspect of Quantum Mechanics has been of great interest recently. There have been numerous studies on non-Hermitian Hamiltonians written for natural processes. Some studies have even expressed the hydrogen atom in a non-Hermitian basis. In this paper, the principles of non-Hermitian quantum mechanics are applied to the time independent perturbation theory and compared with the Zeeman effect. Here, we have also shown the condition under which the Zeeman Effect results will still be true even though the Hamiltonian taken into consideration is non-Hermitian.
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5

Rottoli, Federico, Michele Fossati, and Pasquale Calabrese. "Entanglement Hamiltonian in the non-Hermitian SSH model." Journal of Statistical Mechanics: Theory and Experiment 2024, no. 6 (2024): 063102. http://dx.doi.org/10.1088/1742-5468/ad4860.

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Abstract Entanglement Hamiltonians provide the most comprehensive characterisation of entanglement in extended quantum systems. A key result in unitary quantum field theories is the Bisognano-Wichmann theorem, which establishes the locality of the entanglement Hamiltonian. In this work, our focus is on the non-Hermitian Su-Schrieffer-Heeger (SSH) chain. We study the entanglement Hamiltonian both in a gapped phase and at criticality. In the gapped phase we find that the lattice entanglement Hamiltonian is compatible with a lattice Bisognano-Wichmann result, with an entanglement temperature line
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6

Hallford, Randal, and Preet Sharma. "Non-Hermitian Hamiltonian Treatment of Stark Effect in Quantum Mechanics." Emerging Science Journal 4, no. 6 (2020): 427–35. http://dx.doi.org/10.28991/esj-2020-01242.

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The Non-Hermitian aspect of Quantum Mechanics has been of great interest recently. There have been numerous studies on non-Hermitian Hamiltonians written for natural processes. Some studies have even expressed the hydrogen atom in a non-Hermitian basis. In this paper the principles of non-Hermitian quantum mechanics is applied to both the time independent perturbation theory and to the time dependant theory to calculate the Stark effect. The principles of spherical harmonics has also been used to describe the development in the non-Hermitian case. Finally, the non-Hermitian aspect has been int
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7

BERMAN, GENNADY P., and ALEXANDER I. NESTEROV. "NON-HERMITIAN ADIABATIC QUANTUM OPTIMIZATION." International Journal of Quantum Information 07, no. 08 (2009): 1469–78. http://dx.doi.org/10.1142/s0219749909005961.

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We propose a novel non-Hermitian adiabatic quantum optimization algorithm. One of the new ideas is to use a non-Hermitian auxiliary "initial" Hamiltonian that provides an effective level repulsion for the main Hamiltonian. This effect enables us to develop an adiabatic theory which determines ground state much more efficiently than Hermitian methods.
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8

SINHA, A., and P. ROY. "DARBOUX TRANSFORMATION FOR THE ONE-DIMENSIONAL STATIONARY DIRAC EQUATION WITH NON-HERMITIAN INTERACTION." International Journal of Modern Physics A 21, no. 28n29 (2006): 5807–22. http://dx.doi.org/10.1142/s0217751x0603312x.

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The Darboux algorithm is applied to an exactly solvable one-dimensional stationary Dirac equation, with non-Hermitian, pseudoscalar interaction V0(x). This generates a hierarchy of exactly solvable Dirac Hamiltonians, [Formula: see text], defined by new non-Hermitian interactions V1(x), which are also pseudoscalar. It is shown that [Formula: see text] are isospectral to the initial Hamiltonian h0, except for certain missing states.
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9

Militello, Benedetto, and Anna Napoli. "Evanescent Wave Approximation for Non-Hermitian Hamiltonians." Entropy 22, no. 6 (2020): 624. http://dx.doi.org/10.3390/e22060624.

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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 decay. 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.
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10

Mannheim, Philip D. "PT symmetry as a necessary and sufficient condition for unitary time evolution." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1989 (2013): 20120060. http://dx.doi.org/10.1098/rsta.2012.0060.

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While Hermiticity of a time-independent Hamiltonian leads to unitary time evolution, in and of itself, the requirement of Hermiticity is only sufficient for unitary time evolution. In this paper, we provide conditions that are both necessary and sufficient. We show that symmetry of a time-independent Hamiltonian, or equivalently, reality of the secular equation that determines its eigenvalues, is both necessary and sufficient for unitary time evolution. For any -symmetric Hamiltonian H , there always exists an operator V that relates H to its Hermitian adjoint according to V HV −1 = H † . When
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11

Fring, Andreas, and Rebecca Tenney. "Infinite series of time-dependent Dyson maps." Journal of Physics A: Mathematical and Theoretical 54, no. 48 (2021): 485201. http://dx.doi.org/10.1088/1751-8121/ac31a0.

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Abstract We propose and explore a scheme that leads to an infinite series of time-dependent Dyson maps which associate different Hermitian Hamiltonians to a uniquely specified time-dependent non-Hermitian Hamiltonian. We identify the underlying symmetries responsible for this feature respected by various Lewis–Riesenfeld invariants. The latter are used to facilitate the explicit construction of the Dyson maps and metric operators. As a concrete example for which the scheme is worked out in detail we present a two-dimensional system of oscillators that are coupled to each other in a non-Hermiti
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12

Lechtenfeld, Olaf, and Miloslav Znojil. "Quasi-hermitian quantum mechanics and a new class of user-friendly matrix hamiltonians." Journal of Physics: Conference Series 2667, no. 1 (2023): 012036. http://dx.doi.org/10.1088/1742-6596/2667/1/012036.

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Abstract In the conventional Schrödinger’s formulation of quantum mechanics the unitary evolution of a state ψ is controlled, in Hilbert space L , by a Hamiltonian ɧ which must be self-adjoint. In the recent, “quasi-Hermitian” reformulation of the theory one replaces ɧ by its isospectral but non-Hermitian avatar H = Ω−1 𝖍Ω with Ω†Ω = Θ ≠ I. Although acting in another, manifestly unphysical Hilbert space H , the amended Hamiltonian H ≠ H † can be perceived as self-adjoint with respect to the amended inner-product metric Θ. In our paper motivated by a generic technical “user-unfriendliness” of t
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13

Chen Zeng-Jun and Ning Xi-Jing. "Physical meaning of non-Hermitian Hamiltonian." Acta Physica Sinica 52, no. 11 (2003): 2683. http://dx.doi.org/10.7498/aps.52.2683.

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14

Znojil, Miloslav. "Hermitian–Non-Hermitian Interfaces in Quantum Theory." Advances in High Energy Physics 2018 (2018): 1–12. http://dx.doi.org/10.1155/2018/7906536.

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In the global framework of quantum theory, the individual quantum systems seem clearly separated into two families with the respective manifestly Hermitian and hiddenly Hermitian operators of their Hamiltonian. In the light of certain preliminary studies, these two families seem to have an empty overlap. In this paper, we will show that whenever the interaction potentials are chosen to be weakly nonlocal, the separation of the two families may disappear. The overlapsaliasinterfaces between the Hermitian and non-Hermitian descriptions of a unitarily evolving quantum system in question may becom
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15

De Carlo, Martino, Francesco De Leonardis, Richard A. Soref, Luigi Colatorti, and Vittorio M. N. Passaro. "Non-Hermitian Sensing in Photonics and Electronics: A Review." Sensors 22, no. 11 (2022): 3977. http://dx.doi.org/10.3390/s22113977.

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Recently, non-Hermitian Hamiltonians have gained a lot of interest, especially in optics and electronics. In particular, the existence of real eigenvalues of non-Hermitian systems has opened a wide set of possibilities, especially, but not only, for sensing applications, exploiting the physics of exceptional points. In particular, the square root dependence of the eigenvalue splitting on different design parameters, exhibited by 2 × 2 non-Hermitian Hamiltonian matrices at the exceptional point, paved the way to the integration of high-performance sensors. The square root dependence of the eige
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16

Gavrilik, Alexandre, and Ivan Kachurik. "Pseudo-Hermitian position and momentum operators, Hermitian Hamiltonian, and deformed oscillators." Modern Physics Letters A 34, no. 01 (2019): 1950007. http://dx.doi.org/10.1142/s021773231950007x.

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The recently introduced by us, two- and three-parameter (p, q)- and (p, q, [Formula: see text])-deformed extensions of the Heisenberg algebra were explored under the condition of their direct link with the respective (nonstandard) deformed quantum oscillator algebras. In this paper, we explore certain Hermitian Hamiltonians build in terms of non-Hermitian position and momentum operators obeying definite [Formula: see text](N)-pseudo-hermiticity properties. A generalized nonlinear (with the coefficients depending on the particle number operator N) one-mode Bogoliubov transformation is developed
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17

SERGI, ALESSANDRO, and KONSTANTIN G. ZLOSHCHASTIEV. "NON-HERMITIAN QUANTUM DYNAMICS OF A TWO-LEVEL SYSTEM AND MODELS OF DISSIPATIVE ENVIRONMENTS." International Journal of Modern Physics B 27, no. 27 (2013): 1350163. http://dx.doi.org/10.1142/s0217979213501634.

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We consider a non-Hermitian Hamiltonian in order to effectively describe a two-level system (TLS) coupled to a generic dissipative environment. The total Hamiltonian of the model is obtained by adding a general anti-Hermitian part, depending on four parameters, to the Hermitian Hamiltonian of a tunneling TLS. The time evolution is formulated and derived in terms of the normalized density operator of the model, different types of decays are revealed and analyzed. In particular, the population difference and coherence are defined and calculated analytically. We have been able to mimic various ph
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18

Ramos, B. F., I. A. Pedrosa, and K. Bakke. "Effects of a non-Hermitian potential on the Landau quantization." International Journal of Modern Physics A 34, no. 12 (2019): 1950072. http://dx.doi.org/10.1142/s0217751x19500726.

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In this work, we solve the time-independent Schrödinger equation for a Landau system modulated by a non-Hermitian Hamiltonian. The system consists of a spinless particle in a uniform magnetic field submitted to action of a non-[Formula: see text] symmetric complex potential. Although the Hamiltonian is neither Hermitian nor [Formula: see text]-symmetric, we find that the Landau problem under study exhibits an entirely real energy spectrum.
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19

Lee, Dean. "THE ROLE OF DIAGONALIZATION WITHIN A DIAGONALIZATION/MONTE CARLO SCHEME." International Journal of Modern Physics A 16, supp01c (2001): 1245–47. http://dx.doi.org/10.1142/s0217751x01009430.

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We discuss a method called quasi-sparse eigenvector diagonalization which finds the most important basis vectors of the low energy eigenstates of a quantum Hamiltonian. It can operate using any basis, either orthogonal or non-orthogonal, and any sparse Hamiltonian, either Hermitian, non-Hermitian, finite-dimensional, or infinite-dimensional. The method is part of a new computational approach which combines both diagonalization and Monte Carlo techniques.
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20

Bender, Carl M., Alexander Felski, Sandra P. Klevansky, and Sarben Sarkar. "PT symmetry and renormalisation in quantum field theory." Journal of Physics: Conference Series 2038, no. 1 (2021): 012004. http://dx.doi.org/10.1088/1742-6596/2038/1/012004.

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Abstract Quantum systems governed by non-Hermitian Hamiltonians with PT symmetry are special in having real energy eigenvalues bounded below and unitary time evolution. We argue that PT symmetry may also be important and present at the level of Hermitian quantum field theories because of the process of renormalisation. In some quantum field theories renormalisation leads to PT -symmetric effective Lagrangians. We show how PT symmetry may allow interpretations that evade ghosts and instabilities present in an interpretation of the theory within a Hermitian framework. From the study of examples
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21

Jiang, Tsin-Fu. "Solving Time-Dependent Schödinger Equation for Some PT-Symmetric Quantum Mechanical Problems." Atoms 12, no. 9 (2024): 46. http://dx.doi.org/10.3390/atoms12090046.

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Using a high-precision code, we generate the eigenstates of a PT-symmetric Hamiltonian. We solve the time-dependent Schrödinger equation (TDSE) of the non-Hermitian system based on the eigenset. Since the formulation is relatively new and the observables are calculated differently than conventional quantum mechanics, we justify it with a paradigmatic case in Hermitian quantum mechanics. We present the harmonic generation spectra on some model PT-Hamiltonians driven by an electric pulse. We discuss the physical differences with the harmonic spectra of a pulse-driven atom.
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22

Nininahazwe, Ancilla. "Non Hermitian Matrix Quasi-Exactly Solvable Hamiltonian." Open Journal of Microphysics 08, no. 03 (2018): 15–25. http://dx.doi.org/10.4236/ojm.2018.83003.

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23

Chamberlain, S. R., J. G. Tucker, J. M. Conroy, and H. G. Miller. "Waxman’s algorithm for non-Hermitian Hamiltonian operators." Journal of Physics Communications 2, no. 2 (2018): 025026. http://dx.doi.org/10.1088/2399-6528/aaaea3.

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24

Mazharimousavi, S. Habib. "Non-Hermitian Hamiltonian versusE= 0 localized states." Journal of Physics A: Mathematical and Theoretical 41, no. 24 (2008): 244016. http://dx.doi.org/10.1088/1751-8113/41/24/244016.

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25

Bebiano, N., J. da Providência, S. Nishiyama, and J. P. da Providência. "Fermionic Model with a Non-Hermitian Hamiltonian." Brazilian Journal of Physics 50, no. 2 (2020): 143–52. http://dx.doi.org/10.1007/s13538-019-00729-7.

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26

Faria, C. Figueira de Morisson, and A. Fring. "Time evolution of non-Hermitian Hamiltonian systems." Journal of Physics A: Mathematical and General 39, no. 29 (2006): 9269–89. http://dx.doi.org/10.1088/0305-4470/39/29/018.

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27

Grigorenko, A. N. "Quantum mechanics with a non-Hermitian Hamiltonian." Physics Letters A 172, no. 5 (1993): 350–54. http://dx.doi.org/10.1016/0375-9601(93)90116-h.

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28

MOSTAFAZADEH, ALI. "PSEUDO-HERMITIAN REPRESENTATION OF QUANTUM MECHANICS." International Journal of Geometric Methods in Modern Physics 07, no. 07 (2010): 1191–306. http://dx.doi.org/10.1142/s0219887810004816.

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A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review of the basic ideas and techniques responsible for the recent developments in this subject. We provide a critical assessment of the role of the geometry of the Hilbert space in conventional quantum mechanics to reveal the basic physical principle motivating our study. We then offer a survey of the necessary mathematical tools, present their utility in establ
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29

Zloshchastiev, Konstantin G. "Model Hamiltonians of open quantum optical systems: Evolvement from hermiticity to adjoint commutativity." Journal of Physics: Conference Series 2407, no. 1 (2022): 012011. http://dx.doi.org/10.1088/1742-6596/2407/1/012011.

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Abstract In the conventional quantum mechanics of conserved systems, Hamiltonian is assumed to be a Hermitian operator. However, when it comes to quantum systems in presence of dissipation and/or noise, including open quantum optical systems, the strict hermiticity requirement is nor longer necessary. In fact, it can be substantially relaxed: the non-Hermitian part of a Hamiltonian is allowed, in order to account for effects of dissipative environment, whereas its Hermitian part would be describing subsystem’s energy. Within the framework of the standard approach to dissipative phenomena based
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30

NESTEROV, ALEXANDER I., GENNADY P. BERMAN, and ALAN R. BISHOP. "NON-HERMITIAN DESCRIPTION OF A SUPERCONDUCTING PHASE QUBIT MEASUREMENT." International Journal of Quantum Information 08, no. 06 (2010): 895–904. http://dx.doi.org/10.1142/s0219749910006630.

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We present an approach based on a non-Hermitian Hamiltonian to describe the process of measurement by tunneling of superconducting phase qubit states. We derive simple analytical expressions which describe the dynamics of measurement, and compare our results with those experimentally available. In particular, we show that even for a single qubit, the analytical expressions simplify the analysis of the dynamics in comparison with the density matrix approach. We also demonstrate that the effect of the interference of tunneling channels can be easily described by using the approach based on the n
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31

Kecita, F., A. Bounames, and M. Maamache. "A Real Expectation Value of the Time-dependent Non-Hermitian Hamiltonians*." Physica Scripta 96, no. 12 (2021): 125265. http://dx.doi.org/10.1088/1402-4896/ac3dbd.

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Abstract With the aim to solve the time-dependent Schrödinger equation associated to a time-dependent non-Hermitian Hamiltonian, we introduce a unitary transformation that maps the Hamiltonian to a time-independent   -symmetric one. Consequently, the solution of time-dependent Schrödinger equation becomes easily deduced and the evolution preserves the  ( t ) PT −inner product, where  ( t ) is a obtained from the charge conjugation operator  through a time dependent unitary transformation. Moreover, the expectation value of the non-Hermitian Hamiltonian in the  ( t ) PT normed states is g
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32

Ruschhaupt, Andreas, Miguel A. Simon, Anthony Kiely, and J. Gonzalo Muga. "The Role of Symmetry in Non-Hermitian Scattering1." Journal of Physics: Conference Series 2038, no. 1 (2021): 012020. http://dx.doi.org/10.1088/1742-6596/2038/1/012020.

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Abstract We review recent work on asymmetric scattering by Non-Hermitian (NH) Hamiltonians. Quantum devices with an asymmetric scattering response to particles incident from right or left in effective ID waveguides will be important to develop quantum technologies. They act as microscopic equivalents of familiar macroscopic devices such as diodes, rectifiers, or valves. The symmetry of the underlying NH Hamiltonian leads to selection rules which restrict or allow asymmetric response. NH-symmetry operations may be organized into group structures that determine equivalences among operations once
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33

Geyer, H. B., W. D. Heiss, and F. G. Scholtz. "The physical interpretation of non-Hermitian Hamiltonians and other observables." Canadian Journal of Physics 86, no. 10 (2008): 1195–201. http://dx.doi.org/10.1139/p08-060.

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A recent surge of publications about non-Hermitian Hamiltonians has led to considerable controversy and — in our opinion — to some misunderstandings of basic quantum mechanics. The present paper scrutinizes the metric associated with a quasi-Hermitian Hamiltonian and its physical implications. The consequences of the non-uniqueness such as the question of the probability interpretation and the possible and forbidden choices of additional observables are investigated and exemplified by specific illustrative examples. In particular, it is argued that the improper identification of observables li
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34

Maamache, Mustapha. "NON-UNITARY TRANSFORMATION OF QUANTUM TIME-DEPENDENT NON-HERMITIAN SYSTEMS." Acta Polytechnica 57, no. 6 (2017): 424. http://dx.doi.org/10.14311/ap.2017.57.0424.

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We provide a new perspective on non-Hermitian evolution in quantum mechanics by emphasizing the same method as in the Hermitian quantum evolution. We first give a precise description of the non unitary transformation and the associated evolution, and collecting the basic results around it and postulating the norm preserving. This cautionary postulate imposing that the time evolution of a non Hermitian quantum system preserves the inner products between the associated states must not be read naively. We also give an example showing that the solutions of time-dependent non Hermitian Hamiltonian
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35

Jones-Smith, Katherine. "A ‘Dysonization’ scheme for identifying quasi-particles using non-Hermitian quantum mechanics." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1989 (2013): 20120056. http://dx.doi.org/10.1098/rsta.2012.0056.

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Dyson analysed the low-energy excitations of a ferromagnet using a Hamiltonian that was non-Hermitian with respect to the standard inner product. This allowed for a facile rendering of these excitations (known as spin waves) as weakly interacting bosonic quasi-particles. More than 50 years later, we have the full denouement of the non-Hermitian quantum mechanics formalism at our disposal when considering Dyson’s work, both technically and contextually. Here, we recast Dyson’s work on ferromagnets explicitly in terms of two inner products, with respect to which the Hamiltonian is always self-ad
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BAAQUIE, BELAL E. "ACTION WITH ACCELERATION I: EUCLIDEAN HAMILTONIAN AND PATH INTEGRAL." International Journal of Modern Physics A 28, no. 27 (2013): 1350137. http://dx.doi.org/10.1142/s0217751x13501376.

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An action having an acceleration term in addition to the usual velocity term is analyzed. The quantum mechanical system is directly defined for Euclidean time using the path integral. The Euclidean Hamiltonian is shown to yield the acceleration Lagrangian and the path integral with the correct boundary conditions. Due to the acceleration term, the state space depends on both position and velocity — and hence the Euclidean Hamiltonian depends on two degrees of freedom. The Hamiltonian for the acceleration system is non-Hermitian and can be mapped to a Hermitian Hamiltonian using a similarity tr
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37

VENTRIGLIA, FRANCO. "ALTERNATIVE HAMILTONIAN DESCRIPTIONS FOR QUANTUM SYSTEMS AND NON-HERMITIAN OPERATORS WITH REAL SPECTRUM." Modern Physics Letters A 17, no. 24 (2002): 1589–99. http://dx.doi.org/10.1142/s0217732302007946.

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Many problems in theoretical physics are very frequently dealt with non-Hermitian operators. Recently there has been a lot of interest in non-Hermitian operators with real spectra. In this paper, by using the inverse problem for quantum systems, we show that, on finite-dimensional Hilbert spaces, all diagonalizable operators with a real spectrum can be made Hermitian with respect to a properly chosen inner product. In particular this allows the use of standard methods of quantum mechanics to analyze non-Hermitian operators with real spectra.
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38

Bogoliubov, Nikolai M., and Andrei V. Rybin. "The Generalized Tavis—Cummings Model with Cavity Damping." Symmetry 13, no. 11 (2021): 2124. http://dx.doi.org/10.3390/sym13112124.

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In this Communication, we consider a generalised Tavis–Cummings model when the damping process is taken into account. We show that the quantum dynamics governed by a non-Hermitian Hamiltonian is exactly solvable using the Quantum Inverse Scattering Method, and the Algebraic Bethe Ansatz. The leakage of photons is described by a Lindblad-type master equation. The non-Hermitian Hamiltonian is diagonalised by state vectors, which are elementary symmetric functions parametrised by the solutions of the Bethe equations. The time evolution of the photon annihilation operator is defined via a correspo
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39

Bagchi, Bijan, Rahul Ghosh, and Sauvik Sen. "Analogue Hawking Radiation as a Tunneling in a Two-Level PT-Symmetric System." Entropy 25, no. 8 (2023): 1202. http://dx.doi.org/10.3390/e25081202.

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In light of a general scenario of a two-level non-Hermitian PT-symmetric Hamiltonian, we apply the tetrad-based method to analyze the possibility of analogue Hawking radiation. We carry this out by making use of the conventional null-geodesic approach, wherein the associated Hawking radiation is described as a quantum tunneling process across a classically forbidden barrier on which the event horizon imposes. An interesting aspect of our result is that our estimate for the tunneling probability is independent of the non-Hermitian parameter that defines the guiding Hamiltonian.
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40

Jurić, Tajron, and Hrvoje Nikolić. "Arrival Time from Hamiltonian with Non-Hermitian Boundary Term." Universe 10, no. 1 (2024): 35. http://dx.doi.org/10.3390/universe10010035.

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In this study, we developed a new method for finding the quantum probability density of arrival at the detector. The evolution of the quantum state restricted to the region outside of the detector is described by a restricted Hamiltonian that contains a non-Hermitian boundary term. The non-Hermitian term is shown to be proportional to the flux of the probability current operator through the boundary, which implies that the arrival probability density is equal to the flux of the probability current.
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B, Tuguldur, Zhenhuan Yi, and Jonathan S. Ben-Benjamin. "Effective Raman Hamiltonian revisited." Физик сэтгүүл 32, no. 553 (2022): 1–8. http://dx.doi.org/10.22353/physics.v32i553.561.

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In this paper, the effective Raman Hamiltonian is revisited. A common way to obtain the effective Raman Hamiltonian is by using the time-dependent perturbation method (TDPT) along with Fermi’s golden rule to keep the total energy and probability constant. However, for a non-resonant Raman process the obtained effective Hamiltonian is not convenient because it is not Hermitian. Hence, we present the Magnus expansion method for obtaining the effective Raman Hamiltonian, which has the advantages of being Hermitian and featuring effects absent in the TDPT effective Hamiltonian. To our knowledge, t
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42

ANDRIANOV, A. A., M. V. IOFFE, F. CANNATA, and J. P. DEDONDER. "SUSY QUANTUM MECHANICS WITH COMPLEX SUPERPOTENTIALS AND REAL ENERGY SPECTRA." International Journal of Modern Physics A 14, no. 17 (1999): 2675–88. http://dx.doi.org/10.1142/s0217751x99001342.

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We extend the standard intertwining relations used in supersymmetrical (SUSY) quantum mechanics which involve real superpotentials to complex superpotentials. This allows us to deal with a large class of non-Hermitian Hamiltonians and to study in general the isospectrality between complex potentials. In very specific cases we can construct in a natural way "quasicomplex" potentials which we define as complex potentials having a global property so as to lead to a Hamiltonian with real spectrum. We also obtained a class of complex transparent potentials whose Hamiltonian can be intertwined to a
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43

Alexandre, Jean. "Non-Hermitian Lagrangian for Quasirelativistic Fermions." Advances in Mathematical Physics 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/527967.

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We present a Lorentz-symmetry violating Lagrangian for free fermions, which is local but not Hermitian, whereas the corresponding Hamiltonian is Hermitian but not local. A specific feature of the model is that the dispersion relation is relativistic in both the IR and the UV but not in an intermediate regime, set by a given mass scale. The consistency of the model is shown by the study of properties expected in analogy with the Dirac Lagrangian.
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44

Cao, Yusong, and Junpeng Cao. "Exact Solution of a Non-Hermitian Generalized Rabi Model." Chinese Physics Letters 38, no. 8 (2021): 080202. http://dx.doi.org/10.1088/0256-307x/38/8/080202.

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An integrable non-Hermitian generalized Rabi model is constructed. A twist matrix is introduced to the construction of Hamiltonian and generates the non-Hermitian properties. The Yang-Baxter integrability of the system is proven. The exact energy spectrum and eigenstates are obtained using the Bethe ansatz. The method given in this study provides a general way to construct integrable spin-boson models.
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45

Yang, Frank, Ciril S. Prasad, Weijian Li, Rosemary Lach, Henry O. Everitt, and Gururaj V. Naik. "Non-Hermitian metasurface with non-trivial topology." Nanophotonics 11, no. 6 (2022): 1159–65. http://dx.doi.org/10.1515/nanoph-2021-0731.

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Abstract The synergy between topology and non-Hermiticity in photonics holds immense potential for next-generation optical devices that are robust against defects. However, most demonstrations of non-Hermitian and topological photonics have been limited to super-wavelength scales due to increased radiative losses at the deep-subwavelength scale. By carefully designing radiative losses at the nanoscale, we demonstrate a non-Hermitian plasmonic–dielectric metasurface in the visible with non-trivial topology. The metasurface is based on a fourth order passive parity-time symmetric system. The des
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46

Swanson, Mark S. "Transition elements for a non-Hermitian quadratic Hamiltonian." Journal of Mathematical Physics 45, no. 2 (2004): 585–601. http://dx.doi.org/10.1063/1.1640796.

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Jin, L., and Z. Song. "A physical interpretation for the non-Hermitian Hamiltonian." Journal of Physics A: Mathematical and Theoretical 44, no. 37 (2011): 375304. http://dx.doi.org/10.1088/1751-8113/44/37/375304.

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48

Miniatura, Ch, C. Sire, J. Baudon, and J. Bellissard. "Geometrical Phase Factor for a Non-Hermitian Hamiltonian." Europhysics Letters (EPL) 13, no. 3 (1990): 199–203. http://dx.doi.org/10.1209/0295-5075/13/3/002.

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Miniatura, Ch, C. Sire, J. Baudon, and J. Bellissard. "Geometrical Phase Factor for a Non-Hermitian Hamiltonian." Europhysics Letters (EPL) 14, no. 1 (1991): 91. http://dx.doi.org/10.1209/0295-5075/14/1/017.

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50

Bebiano, N., J. da Providência, S. Nishiyama, and J. P. da Providência. "A quantum system with a non-Hermitian Hamiltonian." Journal of Mathematical Physics 61, no. 8 (2020): 082106. http://dx.doi.org/10.1063/5.0011098.

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