Dissipative dynamics of a harmonic oscillator: A nonperturbative approach

Kumar, Jishad; Sinha, Subhasis; Sreeram, P. A.

doi:10.1103/physreve.80.031130

Cited by 11 publications

(21 citation statements)

References 31 publications

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“…(II. 46). It is clear that the results obtained with the exact Heisenberg-Langevin equations agree with those obtained with the Born-non-Markov quantum master equation when γ/Ω R ≪ 1 and γΛ/Ω 2 ≪ 1.…”

Section: :) Born-markov Approximationsupporting

confidence: 69%

Heisenberg-Langevin versus quantum master equation

Boyanovsky

Jasnow

2017

Phys. Rev. A

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The quantum master equation is an important tool in the study of quantum open systems. It is often derived under a set of approximations, chief among them the Born (factorization) and Markov (neglect of memory effects) approximations. In this article we study the paradigmatic model of quantum Brownian motion of an harmonic oscillator coupled to a bath of oscillators with a Drude-Ohmic spectral density. We obtain analytically the exact solution of the Heisenberg-Langevin equations, with which we study correlation functions in the asymptotic stationary state. We compare the exact correlation functions to those obtained in the asymptotic long time limit with the quantum master equation in the Born approximation with and without the Markov approximation. In the latter case we implement a systematic derivative expansion that yields the exact asymptotic limit under the factorization approximation only. We find discrepancies that could be significant when the bandwidth of the bath Λ is much larger than the typical scales of the system. We study the exact interaction energy as a proxy for the correlations missed by the Born approximation and find that its dependence on Λ is similar to the discrepancy between the exact solution and that of the quantum master equation in the Born approximation. We quantify the regime of validity of the quantum master equation in the Born approximation with or without the Markov approximation in terms of the system's relaxation rate γ, its unrenormalized natural frequency Ω and Λ: γ/Ω ≪ 1 and also γΛ/Ω 2 ≪ 1. The reliability of the Born approximation is discussed within the context of recent experimental settings and more general environments.

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Section: :) Born-markov Approximationsupporting

confidence: 69%

Heisenberg-Langevin versus quantum master equation

Boyanovsky

Jasnow

2017

Phys. Rev. A

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“…Brow (t) being the usual diffusion coefficients [53,85,86], while the flux contribution is again a symmetric anti-diagonal matrix,…”

Section: Single Flux-carrying Brownian Particlementioning

confidence: 99%

“…After integrating by parts the resulting equation from substituting (87) in (86), we recover the familiar continuity equation [42],…”

Section: A Quantum Balance Equationsmentioning

confidence: 99%

Statistical physics of flux-carrying Brownian particles

Valido

2020

Annals of Physics

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We develop the kinetic theory of the flux-carrying Brownian motion recently introduced in the context of open quantum systems. This model constitutes an effective description of two-dimensional dissipative particles violating both time-reversal and parity that is consistent with standard thermodynamics. By making use of an appropriate Breit-Wigner approximation, we derive the general form of its quantum kinetic equation for weak system-environment coupling. This encompasses the well-known Kramers equation of conventional Brownian motion as a particular instance. The influence of the underlying chiral symmetry is essentially twofold: the anomalous diffusive tensor picks up antisymmtretic components, and the drift term has an additional contribution which plays the role of an environmental torque acting upon the system particles. These yield an unconventional fluid dynamics that is absent in the standard (two-dimensional) Brownian motion subject to an external magnetic field or an active torque. For instance, the quantum single-particle system displays a dissipationless vortex flow in sharp contrast with ordinary diffusive fluids. We also provide preliminary results concerning the relevant hydrodynamics quantities, including the fluid vorticity and the vorticity flux, for the dilute scenario near thermal equilibrium. In particular, the flux-carrying effects manifest as vorticity sources in the Kelvin's circulation equation. Conversely, the energy kinetic density remains unchanged and the usual Boyle's law is recovered up to a reformulation of the kinetic temperature.

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“…However, for larger values of the damping constant the many stationary solutions of the system of Eqs. (46)(47)(48) cross, and therefore it is not straightforward to determine the stationary solution of (45) that coincides with the one obtained in the CL limit. Moreover, for larger values of γ the Gaussian ansatz given in Eq.…”

Section: B Stationary State Of the Quadratic Qbmmentioning

confidence: 98%

A Lindblad Model for Quantum Brownian Motion

Lampo

March

Lewenstein

2019

SpringerBriefs in Physics

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The theory of quantum Brownian motion describes the properties of a large class of open quantum systems. Nonetheless, its description in terms of a Born-Markov master equation, widely used in literature, is known to violate the positivity of the density operator at very low temperatures. We study an extension of existing models, leading to an equation in the Lindblad form, which is free of this problem. We study the dynamics of the model, including the detailed properties of its stationary solution, for both constant and position-dependent coupling of the Brownian particle to the bath, focusing in particular on the correlations and the squeezing of the probability distribution induced by the environment.

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Dissipative dynamics of a harmonic oscillator: A nonperturbative approach

Cited by 11 publications

References 31 publications

Heisenberg-Langevin versus quantum master equation

Heisenberg-Langevin versus quantum master equation

Statistical physics of flux-carrying Brownian particles

A Lindblad Model for Quantum Brownian Motion

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