Breaking the symmetry of a Brownian motor with symmetric potentials

Hagman, Henning; Zelán, Martin; Dion, Claude M.

doi:10.1088/1751-8113/44/15/155002

Cited by 5 publications

(2 citation statements)

References 29 publications

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“…In different contexts, the emergence of a current when two potentials are randomly switched, in the presence of Gaussian noise, has been associated to a shift in the position of the minima [15] or to a difference in potential depth [16]. However, it is easy to see that none of these conditions is necessary to produce a current.…”

Section: A Switching Between Two Potentialsmentioning

confidence: 99%

Directed transport induced byα-stable Lévy noises in weakly asymmetric periodic potentials

2013

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We study the motion of a particle in spatially periodic potentials with broken mirror symmetry under the influence of white α-stable Lévy noises. We consider both time-independent and fluctuating potentials. We focus on cases in which the spatial asymmetry of the potential is due not to a difference between the distances from an absolute minimum to the absolute maximum on its left and to the absolute maximum on its right but only to the curvatures of the potential profiles. The analysis is performed using the fractional Fokker-Planck formalism. Consistent results from Langevin simulations are also presented. We analyze the influence of the symmetry properties of the potentials in combination with the fluctuating characteristics of the system in the determination of the current. We find different situations in which both the absolute value and the direction of the current depend not only on the properties of the potential but also on the parameters characterizing the α-stable Lévy noise. Among other features, we analyze the case of supersymmetric potentials. In particular, we show that a static supersymmetric potential produces no current, and we analyze the conditions for observing a nonvanishing current when the potential fluctuates between different supersymmetric profiles.

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Section: A Switching Between Two Potentialsmentioning

confidence: 99%

Directed transport induced byα-stable Lévy noises in weakly asymmetric periodic potentials

2013

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“…For this mechanism to be effective, certain spatiotemporal symmetries [13], supersymmetries [14], and hidden symmetries [15] must be broken. Alternative ways of breaking these symmetries have also been investigated in a two-state Brownian motor, realized with Brownian particles alternating between two phase-shifted, symmetric potentials [16]. It should be noted that, in the traditional rocking ratchet, the friction forces, if any, are assumed to be linear in the velocities of the particles.…”

Section: Introductionmentioning

confidence: 99%

Directed motion of spheres induced by unbiased driving forces in viscous fluids beyond the Stokes' law regime

Casado‐Pascual

2018

Phys. Rev. E

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The emergence of directed motion is investigated in a system consisting of a sphere immersed in a viscous fluid and subjected to time-periodic forces of zero average. The directed motion arises from the combined action of a nonlinear drag force and the applied driving forces, in the absence of any periodic substrate potential. Necessary conditions for the existence of such directed motion are obtained and an analytical expression for the average terminal velocity is derived within the adiabatic approximation. Special attention is paid to the case of two mutually perpendicular forces with sinusoidal time dependence, one with twice the period of the other. It is shown that, although neither of these two forces induces directed motion when acting separately, when added together, the resultant force generates directed motion along the direction of the force with the shortest period. The dependence of the average terminal velocity on the system parameters is analyzed numerically and compared with that obtained using the adiabatic approximation. Among other results, it is found that, for appropriate parameter values, the direction of the average terminal velocity can be reversed by varying the forcing strength. Furthermore, certain aspects of the observed phenomenology are explained by means of symmetry arguments.

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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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Breaking the symmetry of a Brownian motor with symmetric potentials

Cited by 5 publications

References 29 publications

Directed transport induced byα-stable Lévy noises in weakly asymmetric periodic potentials

Directed transport induced byα-stable Lévy noises in weakly asymmetric periodic potentials

Directed motion of spheres induced by unbiased driving forces in viscous fluids beyond the Stokes' law regime

Autonomous Brownian Motor Driven by Nonadiabatic Variation of Internal Parameters

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