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Journal articles on the topic 'Non-Hermitian system'

Author: Grafiati

Published: 4 June 2021

Last updated: 4 February 2022

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1

Liu, Shuo, Ruiwen Shao, Shaojie Ma, et al. "Non-Hermitian Skin Effect in a Non-Hermitian Electrical Circuit." Research 2021 (March 15, 2021): 1–9. http://dx.doi.org/10.34133/2021/5608038.

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The conventional bulk-boundary correspondence directly connects the number of topological edge states in a finite system with the topological invariant in the bulk band structure with periodic boundary condition (PBC). However, recent studies show that this principle fails in certain non-Hermitian systems with broken reciprocity, which stems from the non-Hermitian skin effect (NHSE) in the finite system where most of the eigenstates decay exponentially from the system boundary. In this work, we experimentally demonstrate a 1D non-Hermitian topological circuit with broken reciprocity by utilizing the unidirectional coupling feature of the voltage follower module. The topological edge state is observed at the boundary of an open circuit through an impedance spectra measurement between adjacent circuit nodes. We confirm the inapplicability of the conventional bulk-boundary correspondence by comparing the circuit Laplacian between the periodic boundary condition (PBC) and open boundary condition (OBC). Instead, a recently proposed non-Bloch bulk-boundary condition based on a non-Bloch winding number faithfully predicts the number of topological edge states.

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2

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 become nonempty. This assertion will be illustrated via a few analytically solvable elementary models.

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3

Chernodub, Maxim N., and Alberto Cortijo. "Non-Hermitian Chiral Magnetic Effect in Equilibrium." Symmetry 12, no. 5 (2020): 761. http://dx.doi.org/10.3390/sym12050761.

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We analyze the chiral magnetic effect for non-Hermitian fermionic systems using the bi-orthogonal formulation of quantum mechanics. In contrast to the Hermitian counterparts, we show that the chiral magnetic effect takes place in equilibrium when a non-Hermitian system is considered. The key observation is that for non-Hermitian charged systems, there is no strict charge conservation as understood in Hermitian systems, so the Bloch theorem preventing currents in the thermodynamic limit and in equilibrium does not apply.

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4

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 effectiveness of such a protocol by applying it to physically relevant multi-spin models, showing that the effective non-Hermitian Hamiltonian drives the system to a maximally entangled stationary state. In addition, we report a new recipe to construct a physical scenario where the quantum dynamics of a physical system represented by a given non-Hermitian Hamiltonian model may be simulated. The physical implications and the broad scope potential applications of such a scheme are highlighted.

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5

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 systems given by a linear combination of SU(1,1) and SU(2) are obtained thanks to time-dependent non-unitary transformation.

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6

Xue, Qiufang, Xiaoqing Sun, and Yanting Xiao. "Extrapolated New Hermitian and Skew-Hermitian Splitting Method for Non-Hermitian Positive Definite Linear System." IOP Conference Series: Earth and Environmental Science 428 (January 17, 2020): 012052. http://dx.doi.org/10.1088/1755-1315/428/1/012052.

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7

Santos, Roberto B. B., and Vinícius R. da Silva. "Non-Hermitian model for asymmetric tunneling." Modern Physics Letters B 28, no. 28 (2014): 1450223. http://dx.doi.org/10.1142/s0217984914502236.

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We present a simple non-Hermitian model to describe the phenomenon of asymmetric tunneling between two energy-degenerate sites coupled by a non-reciprocal interaction without dissipation. The system was described using a biorthogonal family of energy eigenvectors, the dynamics of the system was determined by the Schrödinger equation, and unitarity was effectively restored by proper normalization of the state vectors. The results show that the tunneling rates are indeed asymmetrical in this model, leading to an equilibrium that displays unequal occupation of the degenerate systems even in the absence of external interactions.

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8

Wang, C., X. R. Wang, C. X. Guo, and S. P. Kou. "Defective edge states and anomalous bulk-boundary correspondence for topological insulators under non-Hermitian similarity transformation." International Journal of Modern Physics B 34, no. 09 (2020): 2050146. http://dx.doi.org/10.1142/s0217979220501465.

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It was known that for non-Hermitian topological systems due to the non-Hermitian skin effect, the bulk-edge correspondence is broken down. In this paper, by using one-dimensional Su–Schrieffer–Heeger model and two-dimensional (deformed) Qi–Wu–Zhang model as examples, the focus is on a special type of non-Hermitian topological system without non-Hermitian skin effect — topological systems under non-Hermitian similarity transformation. In these non-Hermitian systems, the defective edge states and the breakdown of bulk-edge correspondence are discovered. To characterize the topological properties, a new type of inversion symmetry-protected topological invariant — total [Formula: see text] topological invariant — has been introduced. In topological phases, defective edge states appear. With the help of the effective edge Hamiltonian, it was found that the defective edge states are protected by (generalized) chiral symmetry and thus the (singular) defective edge states are unstable against the perturbation breaking the chiral symmetry. In addition, the results are generalized to non-Hermitian topological insulators with inversion symmetry in higher dimensions. This work could help people to understand the defective edge states and the breakdown of bulk-edge correspondence for non-Hermitian topological systems.

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9

Zheng, Chao, Jin Tian, Daili Li, Jingwei Wen, Shijie Wei, and Yansong Li. "Efficient Quantum Simulation of an Anti-P-Pseudo-Hermitian Two-Level System." Entropy 22, no. 8 (2020): 812. http://dx.doi.org/10.3390/e22080812.

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Besides Hermitian systems, quantum simulation has become a strong tool to investigate non-Hermitian systems, such as PT-symmetric, anti-PT-symmetric, and pseudo-Hermitian systems. In this work, we theoretically investigate quantum simulation of an anti-P-pseudo-Hermitian two-level system in different dimensional Hilbert spaces. In an arbitrary phase, we find that six dimensions are the minimum to construct the anti-P-pseudo-Hermitian two-level subsystem, and it has a higher success probability than using eight dimensions. We find that the dimensions can be reduced further to four or two when the system is in the anti-PT-symmetric or Hermitian phase, respectively. Both qubit-qudit hybrid and pure-qubit systems are able to realize the simulation, enabling experimental implementations in the near future.

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10

Zhou, Longwen. "Non-Hermitian Floquet Phases with Even-Integer Topological Invariants in a Periodically Quenched Two-Leg Ladder." Entropy 22, no. 7 (2020): 746. http://dx.doi.org/10.3390/e22070746.

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Periodically driven non-Hermitian systems could possess exotic nonequilibrium phases with unique topological, dynamical, and transport properties. In this work, we introduce an experimentally realizable two-leg ladder model subjecting to both time-periodic quenches and non-Hermitian effects, which belongs to an extended CII symmetry class. Due to the interplay between drivings and nonreciprocity, rich non-Hermitian Floquet topological phases emerge in the system, with each of them characterized by a pair of even-integer topological invariants ( w 0 , w π ) ∈ 2 Z × 2 Z . Under the open boundary condition, these invariants further predict the number of zero- and π -quasienergy modes localized around the edges of the system. We finally construct a generalized version of the mean chiral displacement, which could be employed as a dynamical probe to the topological invariants of non-Hermitian Floquet phases in the CII symmetry class. Our work thus introduces a new type of non-Hermitian Floquet topological matter, and further reveals the richness of topology and dynamics in driven open systems.

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11

Tian, Zhiyu, Yang Liu, and Le Luo. "Shannon Entropy and Diffusion Coefficient in Parity-Time Symmetric Quantum Walks." Entropy 23, no. 9 (2021): 1145. http://dx.doi.org/10.3390/e23091145.

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Non-Hermitian topological edge states have many intriguing properties, however, to date, they have mainly been discussed in terms of bulk–boundary correspondence. Here, we propose using a bulk property of diffusion coefficients for probing the topological states and exploring their dynamics. The diffusion coefficient was found to show unique features with the topological phase transitions driven by parity–time (PT)-symmetric non-Hermitian discrete-time quantum walks as well as by Hermitian ones, despite the fact that artificial boundaries are not constructed by an inhomogeneous quantum walk. For a Hermitian system, a turning point and abrupt change appears in the diffusion coefficient when the system is approaching the topological phase transition, while it remains stable in the trivial topological state. For a non-Hermitian system, except for the feature associated with the topological transition, the diffusion coefficient in the PT-symmetric-broken phase demonstrates an abrupt change with a peak structure. In addition, the Shannon entropy of the quantum walk is found to exhibit a direct correlation with the diffusion coefficient. The numerical results presented herein may open up a new avenue for studying the topological state in non-Hermitian quantum walk systems.

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12

Singh, Ram Mehar. "Real Eigenvalue of a Non-Hermitian Hamiltonian System." Applied Mathematics 03, no. 10 (2012): 1117–23. http://dx.doi.org/10.4236/am.2012.310164.

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13

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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14

Shakeri, Somayeh, Mohammad-Hossein Zandi, and Alireza Bahrampour. "Tunable photon statistics in a non-Hermitian system." Journal of the Optical Society of America B 34, no. 3 (2017): 566. http://dx.doi.org/10.1364/josab.34.000566.

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15

Bao, Xi-Xi, Gang-Feng Guo, Xue-Peng Du, Huai-Qiang Gu, and Lei Tan. "The topological criticality in disordered non-Hermitian system." Journal of Physics: Condensed Matter 33, no. 18 (2021): 185401. http://dx.doi.org/10.1088/1361-648x/abee3d.

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16

Jeong, Kabgyun, Kyu-Won Park, and Jaewan Kim. "Relative Entropy as a Measure of Difference between Hermitian and Non-Hermitian Systems." Entropy 22, no. 8 (2020): 809. http://dx.doi.org/10.3390/e22080809.

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We employ the relative entropy as a measure to quantify the difference of eigenmodes between Hermitian and non-Hermitian systems in elliptic optical microcavities. We have found that the average value of the relative entropy in the range of the collective Lamb shift is large, while that in the range of self-energy is small. Furthermore, the weak and strong interactions in the non-Hermitian system exhibit rather different behaviors in terms of the relative entropy, and thus it displays an obvious exchange of eigenmodes in the elliptic microcavity.

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17

Jiang, Tianshu, Anan Fang, Zhao-Qing Zhang, and Che Ting Chan. "Anomalous Anderson localization behavior in gain-loss balanced non-Hermitian systems." Nanophotonics 10, no. 1 (2020): 443–52. http://dx.doi.org/10.1515/nanoph-2020-0306.

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AbstractIt has been shown recently that the backscattering of wave propagation in one-dimensional disordered media can be entirely suppressed for normal incidence by adding sample-specific gain and loss components to the medium. Here, we study the Anderson localization behaviors of electromagnetic waves in such gain-loss balanced random non-Hermitian systems when the waves are obliquely incident on the random media. We also study the case of normal incidence when the sample-specific gain-loss profile is slightly altered so that the Anderson localization occurs. Our results show that the Anderson localization in the non-Hermitian system behaves differently from random Hermitian systems in which the backscattering is suppressed.

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18

ANGELOPOULOU, P., S. BASKOUTAS, A. JANNUSSIS, R. MIGNANI, and V. PAPATHEOU. "NON-HERMITIAN TUNNELING OF OPEN QUANTUM SYSTEMS." International Journal of Modern Physics B 09, no. 17 (1995): 2083–104. http://dx.doi.org/10.1142/s0217979295000823.

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We discuss some aspects of the time picture of tunneling for open quantum systems described by non-Hermitian (NH) Hamiltonians. The concept of sojourn time for such systems is introduced in the framework of the biorthonormal formalism. Due to the various definitions of probability density in the non-Hermitian case, we get three different sojourn times, two real and one complex. We consider as model of a dissipative NH system the complex, generalized parametric oscillator, for which we derive the exact expressions of the three sojourn times in terms of the Wei-Norman characteristic functions entering the non-unitary evolution operators. The special case of the inverted Caldirola-Kanai oscillator with complex friction parameter is investigated for an initial extended wavepacket. We also discuss the Landau-Zener-like transitions of the NH parametric oscillator, i.e. the dissipative tunneling through a dynamical barrier due to the perturbative effect of the damping.

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19

Yuce, C. "Topological phase in a non-Hermitian PT symmetric system." Physics Letters A 379, no. 18-19 (2015): 1213–18. http://dx.doi.org/10.1016/j.physleta.2015.02.011.

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20

Thilagam, A. "Non-Hermitian exciton dynamics in a photosynthetic unit system." Journal of Chemical Physics 136, no. 6 (2012): 065104. http://dx.doi.org/10.1063/1.3684654.

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21

Song, Hyun Gyu, Minho Choi, Kie Young Woo, Chung Hyun Park, and Yong-Hoon Cho. "Room-temperature polaritonic non-Hermitian system with single microcavity." Nature Photonics 15, no. 8 (2021): 582–87. http://dx.doi.org/10.1038/s41566-021-00820-z.

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22

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 physical situations with different properties, such as dephasing, vanishing population difference and purification.

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23

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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24

Lu, Xinyang, Qingbiao Wu, and Yasir Khan. "The Analysis of Dynamic Buckling of an Impacted Column using Difference Methods." International Journal of Computational Methods 15, no. 04 (2018): 1850025. http://dx.doi.org/10.1142/s0219876218500251.

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In this paper, the object of our study is two coupled partial differential equation which have a rich physical background. With a reasonable change to the initial value, we use central difference method and compact finite difference method to get the numerical results of the governing equations. In the analysis of the latter, we use the Hermitian and skew-Hermitian splitting (HSS) method to solve a large sparse non-Hermitian positive definite system of linear equations. In this way, the computational efficiency can be improved and the convergence is guaranteed which is proved by Bai [Bai et al. [2003] “Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems,” SIAM J. Matrix Anal. Appl. 24, 603–626] and Chen [Chen et al. [2014] “Convergence analysis of the modified Newton-HSS method under the Hölder continuous condition,” J. Comput. Appl. Math. 264, 115–130]. And we also pay attention to the effect of initial conditions, on which we add a small perturbation to observe its influence by comparing numerical results.

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25

Eleuch, Hichem, and Ingrid Rotter. "Loss, Gain, and Singular Points in Open Quantum Systems." Advances in Mathematical Physics 2018 (September 2, 2018): 1–9. http://dx.doi.org/10.1155/2018/3653851.

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Non-Hermitian quantum physics is used successfully for the description of different puzzling experimental results, which are observed in open quantum systems. Mostly, the influence of exceptional points on the dynamical properties of the system is studied. At these points, two complex eigenvalues Ei≡Ei+iΓi/2 of the non-Hermitian Hamiltonian H coalesce (where Ei is the energy and Γi is the inverse lifetime of the state i). We show that also the eigenfunctions Φi of the two states play an important role, sometimes even the dominant one. Besides exceptional points, other critical points exist in non-Hermitian quantum physics. At these points a=acr in the parameter space, the biorthogonal eigenfunctions of H become orthogonal. For illustration, we show characteristic numerical results.

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26

GIRI, PULAK RANJAN. "CONFORMAL ANOMALY IN NON-HERMITIAN QUANTUM MECHANICS." International Journal of Modern Physics A 25, no. 01 (2010): 155–61. http://dx.doi.org/10.1142/s0217751x10047798.

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A model of an electron and a Dirac monopole interacting in an axially symmetric non-Hermitian but [Formula: see text]-symmetric potential is discussed in detail. The intriguing localization of the wave-packet is observed as a result of the anomalous breaking of the scale symmetry. The symmetry algebra for the system, which is the conformal algebra SO(2, 1), is discussed as a subalgebra of the enveloping algebra of an algebra, composed of the Virasoro algebra, {Ln, n ∈ ℕ} and an Abelian algebra, {Pn, n ∈ ℕ}.

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27

Graefe, Eva Maria, and Hans Jürgen Korsch. "Crossing scenario for a nonlinear non-Hermitian two-level system." Czechoslovak Journal of Physics 56, no. 9 (2006): 1007–20. http://dx.doi.org/10.1007/s10582-006-0396-8.

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28

Weinhold, F. "Time-Conjugation in a Unified Quantum Theory for Hermitian and Non-Hermitian Electronic Systems under Time-Reversal Symmetry." Symmetry 13, no. 5 (2021): 808. http://dx.doi.org/10.3390/sym13050808.

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We propose a reformulation of the mathematical formalism of many-electron quantum theory that rests entirely on the physical properties of the electronic system under investigation, rather than conventional mathematical assumption of Hermitian operators in Hilbert space. The formalism is based on a modified dot-product that replaces the familiar complex-conjugation in Hilbert space ℌ (fixed for all physical systems) by time-conjugation in T-space (as generated by the specific spin, magnetic field, or other explicit t-dependence of the system Hamiltonian ℋ of interest), yielding different spatial structure for different systems. The usual Hermitian requirement for physical operators is thereby generalized to a self-t-adjoint (“t-reversible”) character, leading to correspondingly generalized theorems of virial and hypervirial type. The T-space reformulation preserves the real values of measurable properties and the Born-probabilistic interpretations of state functions that underlie the present quantum theory of measurement, while also properly distinguishing “temporal” behavior of internal decay (tunneling-type) phenomena from that of applied fields with parametric t-dependence on an external clock. The t-product represents a further generalization of the “c-product” that was previously found useful in complex coordinate-rotation studies of autoionizing resonances.

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29

Fu, Ziwei, Nianzu Fu, Huaiyuan Zhang, Zhe Wang, Dong Zhao, and Shaolin Ke. "Extended SSH Model in Non-Hermitian Waveguides with Alternating Real and Imaginary Couplings." Applied Sciences 10, no. 10 (2020): 3425. http://dx.doi.org/10.3390/app10103425.

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We studied the topological properties of an extended Su–Schrieffer–Heeger (SSH) model composed of a binary waveguide array with alternating real and imaginary couplings. The topological invariant of the periodic structures remained quantized with chiral symmetry even though the system was non-Hermitian. The numerical results indicated that phase transition arose when the absolute values of the two couplings were equal. The system supported a topological zero mode at the boundary of nontrivial structures when chiral symmetry was preserved. By adding onsite gain and loss to break chiral symmetry, the topological modes dominated in all supermodes with maximum absolute value of imaginary energy. This study enriches research on the SSH model in non-Hermitian systems and may find applications in optical routers and switches.

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30

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 establishing a lucid and precise formulation of a unitary quantum theory based on a non-Hermitian Hamiltonian, and elaborate on a number of relevant issues of fundamental importance. In particular, we discuss the role of the antilinear symmetries such as [Formula: see text], the true meaning and significance of the so-called charge operators [Formula: see text] and the [Formula: see text]-inner products, the nature of the physical observables, the equivalent description of such models using ordinary Hermitian quantum mechanics, the pertaining duality between local-non-Hermitian versus nonlocal-Hermitian descriptions of their dynamics, the corresponding classical systems, the pseudo-Hermitian canonical quantization scheme, various methods of calculating the (pseudo-) metric operators, subtleties of dealing with time-dependent quasi-Hermitian Hamiltonians and the path-integral formulation of the theory, and the structure of the state space and its ramifications for the quantum Brachistochrone problem. We also explore some concrete physical applications and manifestations of the abstract concepts and tools that have been developed in the course of this investigation. These include applications in nuclear physics, condensed matter physics, relativistic quantum mechanics and quantum field theory, quantum cosmology, electromagnetic wave propagation, open quantum systems, magnetohydrodynamics, quantum chaos and biophysics.

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Cheng Shihang, 程时航, 祝可嘉 Zhu Kejia, and 丁亚琼 Ding Yaqiong. "Diversity Research on Exceptional Points in High Dimensional Non-Hermitian System." Acta Optica Sinica 37, no. 6 (2017): 0626003. http://dx.doi.org/10.3788/aos201737.0626003.

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32

Flores, J. C. "Non-Hermitian Dirac-Fermions and configuration-entropy: A two regime system." Physics Letters A 385 (January 2021): 126987. http://dx.doi.org/10.1016/j.physleta.2020.126987.

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33

Lian-Fu, Wei, and Wang Shun-Jin. "Solving Quantum-Nonautonomous System with Non-Hermitian Hamiltonians by Algebraic Method." Communications in Theoretical Physics 35, no. 1 (2001): 15–18. http://dx.doi.org/10.1088/0253-6102/35/1/15.

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34

Wang, Yan-Yi, and Mao-Fa Fang. "Quantum speed limit time of a non-Hermitian two-level system." Chinese Physics B 29, no. 3 (2020): 030304. http://dx.doi.org/10.1088/1674-1056/ab6c45.

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35

Allilueva, A. I., and A. I. Shafarevich. "Delta-Type Solutions for the Non-Hermitian System of Induction Equations." International Journal of Theoretical Physics 54, no. 11 (2014): 3932–44. http://dx.doi.org/10.1007/s10773-014-2423-z.

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36

Li, Wenlin, Fengyang Zhang, Chong Li, and Heshan Song. "Observation of Non-Hermitian Quantum Correlation Criterion in Mesoscopic Optomechanical System." International Journal of Theoretical Physics 55, no. 4 (2015): 2097–109. http://dx.doi.org/10.1007/s10773-015-2849-y.

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37

Ding, Jian, and Yueke Wang. "Tunable unidirectional reflectionless propagation in non-Hermitian graphene plasmonic waveguide system." Laser Physics 31, no. 2 (2021): 026204. http://dx.doi.org/10.1088/1555-6611/abd55c.

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38

Nanayakkara, A. "Asymptotic behavior of eigen energies of non-Hermitian cubic polynomial systems." Canadian Journal of Physics 85, no. 12 (2007): 1473–80. http://dx.doi.org/10.1139/p07-043.

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The asymptotic behavior of the eigenvalues of a non-Hermitian cubic polynomial system H = (P2/2) + µx3 + ax2 + bx, where µ, a, and b are constant parameters that can be either real or complex, is studied by extending the asymptotic energy expansion method, which has been developed for even degree polynomial systems. Both the complex and the real eigenvalues of the above system are obtained using the asymptotic energy expansion. Quantum eigen energies obtained by the above method are found to be in excellent agreement with the exact eigenvalues. Using the asymptotic energy expansion, analytic expressions for both level spacing distribution and the density of states are derived for the above cubic system. When µ = i, a is real, and b is pure imaginary, it was found that asymptotic energy level spacing increases with the coupling strength a for positive a while it decreases for negative a. PACS Nos.: 03.65.Ge, 04.20.Jb, 03.65.Sq, 02.30.Mv, 05.45

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YOO-KONG, SIKARIN. "THE PATH INTEGRAL APPROACH TO AN N-PARTICLE IN A PT-SYMMETRIC HARMONIC OSCILLATOR." International Journal of Modern Physics B 24, no. 28 (2010): 5579–87. http://dx.doi.org/10.1142/s0217979210056992.

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We study a path integral approach to a system of particles in a PT-symmetric harmonic potential: V(x)=mω2(x2±2iεx)/2. The eigenvalues and eigenstates of the system have been calculated. We find that the total energy of the system is real. The connection between the non-Hermitian and Hermitian Hamiltonians has been discussed and we also establish this connection in the context of path integrals via a considering model.

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40

Larsson, Jonas. "An action principle for the Vlasov equation and associated Lie perturbation equations. Part 2. The Vlasov–Maxwell system." Journal of Plasma Physics 49, no. 2 (1993): 255–70. http://dx.doi.org/10.1017/s0022377800016974.

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An action principle for the Vlasov–Maxwell system in Eulerian field variables is presented. Thus the (extended) particle distribution function appears as one of the fields to be freely varied in the action. The Hamiltonian structures of the Vlasov–Maxwell equations and of the reduced systems associated with small-ampliltude perturbation calculations are easily obtained. Previous results for the linearized Vlasov–Maxwell system are generalized. We find the Hermitian structure also when the background is time-dependent, and furthermore we may now also include the case of non-Hamiltonian perturbations within the Hamiltonian-Hermitian context. The action principle for the Vlasov–Maxwell system appears to be suitable for the derivation of reduced dynamical equations by expanding the action in various small parameters.

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Lin, Kunsong, Jiaxiao Zhu, and Yunxia Chen. "A non-Hermitian quantum approach to reliability of a two-state system." Physics Letters A 384, no. 10 (2020): 126207. http://dx.doi.org/10.1016/j.physleta.2019.126207.

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Wang, Haiwen, Sid Assawaworrarit, and Shanhui Fan. "Dynamics for encircling an exceptional point in a nonlinear non-Hermitian system." Optics Letters 44, no. 3 (2019): 638. http://dx.doi.org/10.1364/ol.44.000638.

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Zhang, X. Z., G. Zhang, and Z. Song. "Classical correspondence of the exceptional points in the finite non-Hermitian system." Journal of Physics A: Mathematical and Theoretical 52, no. 16 (2019): 165302. http://dx.doi.org/10.1088/1751-8121/ab0ede.

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Zhang, X. Z., and Z. Song. "Momentum-independent reflectionless transmission in the non-Hermitian time-reversal symmetric system." Annals of Physics 339 (December 2013): 109–21. http://dx.doi.org/10.1016/j.aop.2013.08.012.

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45

Bao, Xi-Xi, Gang-Feng Guo, and Lei Tan. "Exploration of the topological properties in a non-Hermitian long-range system." Journal of Physics: Condensed Matter 33, no. 46 (2021): 465403. http://dx.doi.org/10.1088/1361-648x/ac2040.

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Wagner, Marcel, Felix Dangel, Holger Cartarius, Jörg Main, and Günter Wunner. "NUMERICAL CALCULATION OF THE COMPLEX BERRY PHASE IN NON-HERMITIAN SYSTEMS." Acta Polytechnica 57, no. 6 (2017): 470. http://dx.doi.org/10.14311/ap.2017.57.0470.

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We numerically investigate topological phases of periodic lattice systems in tight-binding description under the influence of dissipation. The effects of dissipation are effectively described by <em>PT</em>-symmetric potentials. In this framework we develop a general numerical gauge smoothing procedure to calculate complex Berry phases from the biorthogonal basis of the system's non-Hermitian Hamiltonian. Further, we apply this method to a one-dimensional <em>PT</em>-symmetric lattice system and verify our numerical results by an analytical calculation.

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Shubin, Nikolay, Alexander Gorbatsevich, and Gennadiy Krasnikov. "Non-Hermitian Hamiltonians and Quantum Transport in Multi-Terminal Conductors." Entropy 22, no. 4 (2020): 459. http://dx.doi.org/10.3390/e22040459.

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We study the transport properties of multi-terminal Hermitian structures within the non-equilibrium Green’s function formalism in a tight-binding approximation. We show that non-Hermitian Hamiltonians naturally appear in the description of coherent tunneling and are indispensable for the derivation of a general compact expression for the lead-to-lead transmission coefficients of an arbitrary multi-terminal system. This expression can be easily analyzed, and a robust set of conditions for finding zero and unity transmissions (even in the presence of extra electrodes) can be formulated. Using the proposed formalism, a detailed comparison between three- and two-terminal systems is performed, and it is shown, in particular, that transmission at bound states in the continuum does not change with the third electrode insertion. The main conclusions are illustratively exemplified by some three-terminal toy models. For instance, the influence of the tunneling coupling to the gate electrode is discussed for a model of quantum interference transistor. The results of this paper will be of high interest, in particular, within the field of quantum design of molecular electronic devices.

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Miri, Mohammad-Ali, and Andrea Alù. "Exceptional points in optics and photonics." Science 363, no. 6422 (2019): eaar7709. http://dx.doi.org/10.1126/science.aar7709.

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Exceptional points are branch point singularities in the parameter space of a system at which two or more eigenvalues, and their corresponding eigenvectors, coalesce and become degenerate. Such peculiar degeneracies are distinct features of non-Hermitian systems, which do not obey conservation laws because they exchange energy with the surrounding environment. Non-Hermiticity has been of great interest in recent years, particularly in connection with the quantum mechanical notion of parity-time symmetry, after the realization that Hamiltonians satisfying this special symmetry can exhibit entirely real spectra. These concepts have become of particular interest in photonics because optical gain and loss can be integrated and controlled with high resolution in nanoscale structures, realizing an ideal playground for non-Hermitian physics, parity-time symmetry, and exceptional points. As we control dissipation and amplification in a nanophotonic system, the emergence of exceptional point singularities dramatically alters their overall response, leading to a range of exotic optical functionalities associated with abrupt phase transitions in the eigenvalue spectrum. These concepts enable ultrasensitive measurements, superior manipulation of the modal content of multimode lasers, and adiabatic control of topological energy transfer for mode and polarization conversion. Non-Hermitian degeneracies have also been exploited in exotic laser systems, new nonlinear optics schemes, and exotic scattering features in open systems. Here we review the opportunities offered by exceptional point physics in photonics, discuss recent developments in theoretical and experimental research based on photonic exceptional points, and examine future opportunities in this area from basic science to applied technology.

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Mostafazadeh, Ali. "Time-Dependent Pseudo-Hermitian Hamiltonians and a Hidden Geometric Aspect of Quantum Mechanics." Entropy 22, no. 4 (2020): 471. http://dx.doi.org/10.3390/e22040471.

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A non-Hermitian operator H defined in a Hilbert space with inner product ⟨ · | · ⟩ may serve as the Hamiltonian for a unitary quantum system if it is η -pseudo-Hermitian for a metric operator (positive-definite automorphism) η . The latter defines the inner product ⟨ · | η · ⟩ of the physical Hilbert space H η of the system. For situations where some of the eigenstates of H depend on time, η becomes time-dependent. Therefore, the system has a non-stationary Hilbert space. Such quantum systems, which are also encountered in the study of quantum mechanics in cosmological backgrounds, suffer from a conflict between the unitarity of time evolution and the unobservability of the Hamiltonian. Their proper treatment requires a geometric framework which clarifies the notion of the energy observable and leads to a geometric extension of quantum mechanics (GEQM). We provide a general introduction to the subject, review some of the recent developments, offer a straightforward description of the Heisenberg-picture formulation of the dynamics for quantum systems having a time-dependent Hilbert space, and outline the Heisenberg-picture formulation of dynamics in GEQM.

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Grimaldi, Andrea, Alessandro Sergi, and Antonino Messina. "Evolution of a Non-Hermitian Quantum Single-Molecule Junction at Constant Temperature." Entropy 23, no. 2 (2021): 147. http://dx.doi.org/10.3390/e23020147.

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This work concerns the theoretical description of the quantum dynamics of molecular junctions with thermal fluctuations and probability losses. To this end, we propose a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments. Along the lines discussed in [A. Sergi et al., Symmetry 10 518 (2018)], we adopt the operator-valued Wigner formulation of quantum mechanics (wherein the density matrix depends on the points of the Wigner phase space associated to the system) and derive a non-linear equation of motion. Moreover, we introduce a model for a non-Hermitian quantum single-molecule junction (nHQSMJ). In this model the leads are mapped to a tunneling two-level system, which is in turn coupled to a harmonic mode (i.e., the molecule). A decay operator acting on the two-level system describes phenomenologically probability losses. Finally, the temperature of the molecule is controlled by means of a Nosé-Hoover chain thermostat. A numerical study of the quantum dynamics of this toy model at different temperatures is reported. We find that the combined action of probability losses and thermal fluctuations assists quantum transport through the molecular junction. The possibility that the formalism here presented can be extended to treat both more quantum states (∼10) and many more classical modes or atomic particles (∼103−105) is highlighted.

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