On the invariant method for the time-dependent non-Hermitian Hamiltonians

Khantoul, Boubakeur; Bounames, A.; Maamache, M.

doi:10.1140/epjp/i2017-11524-7

Cited by 54 publications

(39 citation statements)

References 28 publications

(46 reference statements)

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“…As for Lewis-Riesenfeld invariants for Non-Hermitian Hamiltonians, they can be generalized in two different forms (Simón et al, 2018) corresponding to (Gao et al, 1992;Khantoul et al, 2017;)…”

Section: Non-hermitian Hamiltoniansmentioning

confidence: 99%

Shortcuts to adiabaticity: Concepts, methods, and applications

et al. 2019

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Shortcuts to adiabaticity (STA) are fast routes to the final results of slow, adiabatic changes of the controlling parameters of a system. The shortcuts are designed by a set of analytical and numerical methods suitable for different systems and conditions. A motivation to apply STA methods to quantum systems is to manipulate them on timescales shorter than decoherence times. Thus shortcuts to adiabaticity have become instrumental in preparing and driving internal and motional states in atomic, molecular, and solid-state physics. Applications range from information transfer and processing based on gates or analog paradigms, to interferometry and metrology. The multiplicity of STA paths for the controlling parameters may be used to enhance robustness versus noise and perturbations, or to optimize relevant variables. Since adiabaticity is a widespread phenomenon, STA methods also extended beyond the quantum world, to optical devices, classical mechanical systems, and statistical physics. Shortcuts to adiabaticity combine well with other concepts and techniques, in particular with optimal control theory, and pose fundamental scientific and engineering questions such as finding speed limits, quantifying the third law, or determining process energy costs and efficiencies. We review concepts, methods and applications of shortcuts to adiabaticity and outline promising prospects, as well as open questions and challenges ahead.

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Section: Non-hermitian Hamiltoniansmentioning

confidence: 99%

Shortcuts to adiabaticity: Concepts, methods, and applications

et al. 2019

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“…It is precisely this omission that we aim to remedy here. This technical complexity also probably explains why only a relatively few realistic applications of several alternative implementations of the NHIP ideas themselves may yet be found in the current literature [30,[72][73][74][75][76][77][78][79][80][81].…”

Section: B the Physical Hilbert Space Metric Operatormentioning

confidence: 99%

Non-Hermitian coupled cluster method for non-stationary systems and its interaction-picture reinterpretation

Bishop

Znojil

2020

Eur. Phys. J. Plus

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The interaction picture in a non-Hermitian realization is discussed in detail and considered for its practical use in many-body quantum physics. The resulting non-Hermitian interaction-picture (NHIP) description of dynamics, in which both the wave functions and operators belonging to physical observables cease to remain constant in time, is a non-Hermitian generalization of the traditional Dirac picture of standard quantum mechanics, which itself is widely used in quantum field theory calculations. Particular attention is also paid here to the variational (or, better, bivariational) and dynamical (i.e., non-stationary) aspects that are characteristic of the coupled cluster method (CCM) techniques that nowadays form one of the most versatile and most accurate of all available formulations of quantum many-body theory. In so doing we expose and exploit multiple parallels between the NHIP and the CCM in its time-dependent versions. * raymond.bishop@manchester.ac.uk † znojil@ujf.cas.cz

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“…The most efficient way to solve the time-dependent Dyson equation (1.3) is to use the Lewis-Riesenfeld approach [27] and compute at first the respective time-dependent invariants I h (t) and I H (t) for the Hamiltonian h(t) and H(t), see [28,29,22], by solving the equations…”

Section: Quasi-exactly Solvable Lewis-riesenfeld Invariantsmentioning

confidence: 99%

Quasi-exactly solvable quantum systems with explicitly time-dependent Hamiltonians

Fring

Frith

2019

Physics Letters A

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For a large class of time-dependent non-Hermitain Hamiltonians expressed in terms linear and bilinear combinations of the generators for an Euclidean Lie-algebra respecting different types of PT-symmetries, we find explicit solutions to the time-dependent Dyson equation. A specific Hermitian model with explicit time-dependence is analyzedfurther and shown to be quasi-exactly solvable. Technically we constructed the Lewis-Riesenfeld invariants making use of the metric picture, which is an equivalent alternative to the Schrödinger, Heisenberg and interaction picture containing the time-dependence in the metric operator that relates the time-dependent Hermitian Hamiltonian to a static non-Hermitian Hamiltonian.

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On the invariant method for the time-dependent non-Hermitian Hamiltonians

Cited by 54 publications

References 28 publications

Shortcuts to adiabaticity: Concepts, methods, and applications

Shortcuts to adiabaticity: Concepts, methods, and applications

Non-Hermitian coupled cluster method for non-stationary systems and its interaction-picture reinterpretation

Quasi-exactly solvable quantum systems with explicitly time-dependent Hamiltonians

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