Quantum and classical statistical mechanics of a class of non-Hermitian Hamiltonians

Jones, H. F.; Moreira, E. S.

doi:10.1088/1751-8113/43/5/055307

Cited by 22 publications

(24 citation statements)

References 36 publications

(65 reference statements)

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“…One speaks of broken PT symmetry, and the EP marks the position of the PT symmetry breaking. Since the occurrence of exceptional points is a generic feature of the PT phase transition a large number of works exists for PT -symmetric quantum mechanics [27,[34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49], quantum field theories [50,51], electromagnetic waves [52][53][54][55][56][57][58], and electronic devices [59].…”

Section: Introductionmentioning

confidence: 99%

Simple Models of Three Coupled Pt -Symmetric Wave Guides Allowing for Third-Order Exceptional Points

Schnabel¹,

Cartarius²,

Main³

et al. 2017

Acta Polytech

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Abstract.We study theoretical models of three coupled wave guides with a PT -symmetric distribution of gain and loss. A realistic matrix model is developed in terms of a three-mode expansion. By comparing with a previously postulated matrix model it is shown how parameter ranges with good prospects of finding a third-order exceptional point (EP3) in an experimentally feasible arrangement of semiconductors can be determined. In addition it is demonstrated that continuous distributions of exceptional points, which render the discovery of the EP3 difficult, are not only a feature of extended wave guides but appear also in an idealised model of infinitely thin guides shaped by delta functions.

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Section: Introductionmentioning

confidence: 99%

Simple Models of Three Coupled Pt -Symmetric Wave Guides Allowing for Third-Order Exceptional Points

Schnabel¹,

Cartarius²,

Main³

et al. 2017

Acta Polytech

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“…The theoretical investigations are also undergoing rapid developments: non-Hermitian quantum mechanics has been investigated within a relativistic framework [31] and it has been adopted by various researchers as a means to describe open quantum systems [32][33][34][35][36][37][38][39][40][41][42]. Moreover, it seems that a few theoretical studies have been dedicated to the statistical mechanics and dynamics of systems with non-Hermitian Hamiltonians [43][44][45][46][47][48][49][50][51][52][53][54].…”

Section: Introductionmentioning

confidence: 99%

Embedding quantum systems with a non-conserved probability in classical environments

Sergi

2015

Theor Chem Acc

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Quantum systems with a non-conserved probability can be described by means of non-HermitianHamiltonians and non-unitary dynamics. In this paper, the case in which the degrees of freedom can be partitioned in two subsets with light and heavy masses is treated. A classical limit over the heavy coordinates is taken in order to embed the non-unitary dynamics of the subsystem in a classical environment. Such a classical environment, in turn, acts as an additional source of dissipation (or noise), beyond that represented by the non-unitary evolution. The non-Hermitian dynamics of a Heisenberg two-spin chain, with the spins independently coupled to harmonic oscillators, is considered in order to illustrate the formalism.

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“…Non-Hermitian quantum dynamics differ drastically from their unitary counterparts, and their generic features are far from being fully understood. In particular, the investigation of the quantum classical correspondence for non-Hermitian systems is only at its beginning [22,[36][37][38][39][40].…”

Section: Introductionmentioning

confidence: 99%

Quantum-classical correspondence for a non-Hermitian Bose-Hubbard dimer

2010

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We investigate the many-particle and mean-field correspondence for a non-Hermitian N-particle BoseHubbard dimer where a complex onsite energy describes an effective decay from one of the modes. Recently a generalized mean-field approximation for this non-Hermitian many-particle system yielding an alternative complex nonlinear Schrödinger equation was introduced. Here we give details of this mean-field approximation and show that the resulting dynamics can be expressed in a generalized canonical form that includes a metric gradient flow. The interplay of nonlinearity and non-Hermiticity introduces a qualitatively new behavior to the mean-field dynamics: The presence of the non-Hermiticity promotes the self-trapping transition, while damping the self-trapping oscillations, and the nonlinearity introduces a strong sensitivity to the initial conditions in the decay of the normalization. Here we present a complete characterization of the mean-field dynamics and the fixed point structure. We also investigate the full many-particle dynamics, which shows a rich variety of breakdown and revival as well as tunneling phenomena on top of the mean-field structure.

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Quantum and classical statistical mechanics of a class of non-Hermitian Hamiltonians

Cited by 22 publications

References 36 publications

Simple Models of Three Coupled Pt -Symmetric Wave Guides Allowing for Third-Order Exceptional Points

Simple Models of Three Coupled Pt -Symmetric Wave Guides Allowing for Third-Order Exceptional Points

Embedding quantum systems with a non-conserved probability in classical environments

Quantum-classical correspondence for a non-Hermitian Bose-Hubbard dimer

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