The Schrödinger equation with friction from the quantum trajectory perspective

Garashchuk, Sophya; Dixit, Vaibhav; Gu, Bing; Mazzuca, James W.

doi:10.1063/1.4788832

Cited by 33 publications

(34 citation statements)

References 23 publications

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“…Apart from the fundamental aspect related to the quantum equilibrium hypothesis, in the literature it is also possible to find different works with a more practical orientation, where Bohmian mechanics is used as a tool to explore and analyze the relaxation dynamics of quantum systems [295][296][297][298][299][300][301][302][303]. Similarly, the appealing feature of dealing with ensembles has also been considered to develop semiclassical-like statistical numerical approaches [304][305][306][307].…”

Section: Relaxation and Quantum Equilibriummentioning

confidence: 99%

Applied Bohmian mechanics

et al. 2014

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Abstract. Bohmian mechanics provides an explanation of quantum phenomena in terms of point-like particles guided by wave functions. This review focuses on the use of nonrelativistic Bohmian mechanics to address practical problems, rather than on its interpretation. Although the Bohmian and standard quantum theories have different formalisms, both give exactly the same predictions for all phenomena. Fifteen years ago, the quantum chemistry community began to study the practical usefulness of Bohmian mechanics. Since then, the scientific community has mainly applied it to study the (unitary) evolution of single-particle wave functions, either by developing efficient quantum trajectory algorithms or by providing a trajectorybased explanation of complicated quantum phenomena. Here we present a large list of examples showing how the Bohmian formalism provides a useful solution in different forefront research fields for this kind of problems (where the Bohmian and the quantum hydrodynamic formalisms coincide). In addition, this work also emphasizes that the Bohmian formalism can be a useful tool in other types of (nonunitary and nonlinear) quantum problems where the influence of the environment or the nonsimulated degrees of freedom are relevant. This review contains also examples on the use of the Bohmian formalism for the many-body problem, decoherence and measurement processes. The ability of the Bohmian formalism to analyze this last type of problems for (open) quantum systems remains mainly unexplored by the scientific community. The authors of this review are convinced that the final status of the Bohmian theory among the scientific community will be greatly influenced by its potential success in those types of problems that present nonunitary and/or nonlinear quantum evolutions. A brief introduction of the Bohmian formalism and some of its extensions are presented in the last part of this review.

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Section: Relaxation and Quantum Equilibriummentioning

confidence: 99%

Applied Bohmian mechanics

et al. 2014

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“…The study of its solutions without stochastic term has been carried out in many specific cases, either analytically [18,31,32,41,42,43,44,45,46] or numerically [24,33,41,47,48,49,50,51]. Along these analysis, it has been advocated that the stationary eigenstates of H 0 are also stationary states of the equation [18,43].…”

Section: Introductionmentioning

confidence: 99%

“…A nonlinear friction can be obtained by extending Kostin derivation to a nonlinear coupling [28,29]. The SLE exhibits interesting properties: unitarity is preserved at all times [24], the uncertainty principle is always satisfied 2 [31,32,33] and the superposition principle is violated due to the nonlinearities (which might not be a problem per se for dissipative equations [34,35]). Thanks to its straightforward formulation -in principle only two "classical" parameters need to be known: the friction coefficient A and the bath temperature T bath -and its numerical simplicity, the SLE can be considered as a solid candidate for effective description of open quantum systems hardly accessible to quantum master equations [14,36].…”

Section: Introductionmentioning

confidence: 99%

“…The practical application of the HLE is nevertheless limited by its non-commutating operator nature. The SLE has also been derived within many other frameworks and non-standard quantization procedures to describe either pure dissipation [18,19,20,21,22,23,24] or the case of a Brownian motion [25,26,27]. The SLE includes a thermal fluctuation term −xF R (t) and a dissipative term under its hydrodynamic formulation [20,24,25] A(S(x, t) − S ),…”

Section: Introductionmentioning

confidence: 99%

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The Schrödinger–Langevin equation with and without thermal fluctuations

2016

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The Schrödinger-Langevin equation (SLE) is considered as an effective open quantum system formalism suitable for phenomenological applications involving a quantum subsystem interacting with a thermal bath. We focus on two open issues relative to its solutions: the stationarity of the excited states of the non-interacting subsystem when one considers the dissipation only and the thermal relaxation toward asymptotic distributions with the additional stochastic term. We first show that a proper application of the Madelung/polar transformation of the wave function leads to a non zero damping of the excited states of the quantum subsystem. We then study analytically and numerically the SLE ability to bring a quantum subsystem to the thermal equilibrium of statistical mechanics. To do so, concepts about statistical mixed states and quantum noises are discussed and a detailed analysis is carried with two kinds of noise and potential. We show that within our assumptions the use of the SLE as an effective open quantum system formalism is possible and discuss some of its limitations.

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“…1. There are many reports in connection with quantum dissipation [5,6,8,[16][17][18][19][20][21][22][23][24][25][26]. Fujii and Suzuki studied Jaynes-Cummings model for quantum dissipative systems [18,19].…”

Section: Resultsmentioning

confidence: 99%

Quantum Analysis of a Modified Caldirola-Kanai Oscillator Model for Electromagnetic Fields in Time-Varying Plasma

Choi¹,

Lakehal²,

Maamache³

et al. 2014

PIER Letters

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Abstract-Quantum properties of a modified Caldirola-Kanai oscillator model for propagating electromagnetic fields in a plasma medium are investigated using invariant operator method. As a modification, ordinary exponential function in the Hamiltonian is replaced with a modified exponential function, so-called the q-exponential function. The system described in terms of q-exponential function exhibits nonextensivity. Characteristics of the quantized fields, such as quantum electromagnetic energy, quadrature fluctuations, and uncertainty relations are analyzed in detail in the Fock state, regarding the q-exponential function. We confirmed, from their illustrations, that these quantities oscillate with time in some cases. It is shown from the expectation value of energy operator that quantum energy of radiation fields dissipates with time, like a classical energy, on account of the existence of non-negligible conductivity in media.

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The Schrödinger equation with friction from the quantum trajectory perspective

Cited by 33 publications

References 23 publications

Applied Bohmian mechanics

Applied Bohmian mechanics

The Schrödinger–Langevin equation with and without thermal fluctuations

Quantum Analysis of a Modified Caldirola-Kanai Oscillator Model for Electromagnetic Fields in Time-Varying Plasma

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