Nonlinear dissipation effect in Brownian relaxation

Plyukhin, A. V.; Froese, Aaron

doi:10.1103/physreve.76.031121

Cited by 15 publications

(36 citation statements)

References 27 publications

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“…It has been shown that the stationary probability distribution function (PDF) is independent of magnitudes of additive and multiplicative noises and of the relaxation time of colored noise [20][21][22]29], although the response to applied input depends on noise parameters [29]. This is in contrast with previous studies [30][31][32] which show that the stationary PDF of the Langevin model for the harmonic potential is Gaussian or non-Gaussian, depending on magnitudes of additive and multiplicative noises.…”

Section: Introductioncontrasting

confidence: 54%

“…We consider a system of a Brownian particle coupled to a bath consisting of N -body uncoupled oscillators, which is described by the generalized CL model [20][21][22]29],…”

Section: A Non-markovian Langevin Equationmentioning

confidence: 99%

“…By using the generalized CL model including a nonlinear system-bath coupling, we may obtain the non-Markovian Langevin equation with multiplicative noise which preserves the FDR [18,19]. The nature of nonlinear dissipation and multiplicative noise has been recently explored with renewed interest [20][21][22]. Nonlinear dissipation and multiplicative noise have been recognized as important ingredients in several fields such as mesoscopic scale systems [23,24] and ratchet problems [25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

“…This is in contrast with previous studies [30][31][32] which show that the stationary PDF of the Langevin model for the harmonic potential is Gaussian or non-Gaussian, depending on magnitudes of additive and multiplicative noises. We expect that when the generalized CL model with a nonlinear coupling [20][21][22]29] is applied to a bistable system, properties of the calculated SR may be rather different from those having been derived by the phenomenological Langevin models [4,[6][7][8][9][10][11][12][13][14]. It is the purpose of the present paper to make a detailed study on SR of an open bistable system described by the microscopic, generalized CL model with nonlinear nonlocal dissipation and state-dependent diffusion [29].…”

Section: Introductionmentioning

confidence: 99%

“…In Sec. II, we briefly summarize the non-Markovian Langevin equation derived from the generalized CL model with OU colored noise [20][21][22]29].…”

Section: Introductionmentioning

confidence: 99%

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Stochastic resonance in bistable systems with nonlinear dissipation and multiplicative noise: A microscopic approach

Hasegawa

2013

Physica A: Statistical Mechanics and its Applications

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The stochastic resonance (SR) in bistable systems has been extensively discussed with the use of phenomenological Langevin models. By using the microscopic, generalized Caldeira-Leggett (CL) model, we study in this paper, SR of an open bistable system coupled to a bath with a nonlinear system-bath interaction. The adopted CL model yields the non-Markovian Langevin equation with nonlinear dissipation and state-dependent diffusion which preserve the fluctuationdissipation relation (FDR). From numerical calculations, we find the following: (1) the spectral power amplification (SPA) exhibits SR not only for a and b but also for τ while the stationary probability distribution function is independent of them where a (b) denotes the magnitude of multiplicative (additive) noise and τ expresses the relaxation time of colored noise; (2) the SPA for coexisting additive and multiplicative noises has a single-peak but two-peak structure as functions of a, b and/or τ . These results (1) and (2)

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Section: Introductioncontrasting

confidence: 54%

“…We consider a system of a Brownian particle coupled to a bath consisting of N -body uncoupled oscillators, which is described by the generalized CL model [20][21][22]29],…”

Section: A Non-markovian Langevin Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In Sec. II, we briefly summarize the non-Markovian Langevin equation derived from the generalized CL model with OU colored noise [20][21][22]29].…”

Section: Introductionmentioning

confidence: 99%

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Stochastic resonance in bistable systems with nonlinear dissipation and multiplicative noise: A microscopic approach

Hasegawa

2013

Physica A: Statistical Mechanics and its Applications

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Autonomous Brownian Motor Driven by Nonadiabatic Variation of Internal Parameters

Plyukhin

2015

J Stat Phys

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We discuss an autonomous motor based on a Brownian particle driven from thermal equilibrium by periodic in time variation of the internal potential through which the particle interacts with molecules of the surrounding thermal bath. We demonstrate for such a motor the absence of a linear response regime: The average driving force and drift velocity are shown to be quadratic in both the frequency and amplitude of the variation. The adiabatic approximation (of an infinitely slow variation) and the leading correction to it (linear in the variation's frequency) both lead to zero drift and are insufficient to describe the motor's operation.

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Coulomb Friction Driving Brownian Motors

Manacorda¹,

Puglisi²,

Sarracino³

2014

Commun. Theor. Phys.

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We review a family of models recently introduced to describe Brownian motors under the influence of Coulomb friction, or more general non-linear friction laws. It is known that, if the heat bath is modeled as the usual Langevin equation (linear viscosity plus white noise), additional non-linear friction forces are not sufficient to break detailed balance, i.e. cannot produce a motor effect. We discuss two possibile mechanisms to elude this problem. A first possibility, exploited in several models inspired to recent experiments, is to replace the heat bath's white noise by a "collisional noise", that is the effect of random collisions with an external equilibrium gas of particles. A second possibility is enlarging the phase space, e.g. by adding an external potential which couples velocity to position, as in a Klein-Kramers equation.In both cases, non-linear friction becomes sufficient to achieve a non-equilibrium steady state and, in the presence of an even small spatial asymmetry, a motor effect is produced.

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Nonlinear dissipation effect in Brownian relaxation

Cited by 15 publications

References 27 publications

Stochastic resonance in bistable systems with nonlinear dissipation and multiplicative noise: A microscopic approach

Stochastic resonance in bistable systems with nonlinear dissipation and multiplicative noise: A microscopic approach

Autonomous Brownian Motor Driven by Nonadiabatic Variation of Internal Parameters

Coulomb Friction Driving Brownian Motors

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