Brownian motor with competing spatial and temporal asymmetry of potential energy

Розенбаум, В. М.; Korochkova, T. Ye.; Chernova, A. A.; Dekhtyar, M. L.

doi:10.1103/physreve.83.051120

Cited by 38 publications

(31 citation statements)

References 34 publications

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“…For the case of Gaussian noise (i.e., α = 2), the effect was previously reported in Ref. [15]. In that work, the emergence of a current for a system that switches between two symmetric potentials at equal rates has been linked to the fact that the maxima and minima of both potentials are shifted relatively to each other.…”

Section: A Switching Between Two Potentialssupporting

confidence: 56%

“…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%

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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 Potentialssupporting

confidence: 56%

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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“…The adiabaticity condition implies that (i) transitions from V a (x) to V b (x) and vice versa are fast, and (ii) the particle residence times in states a and b, τ a and τ b , are large as compared to all characteristic times of the system. With these conditions satisfied, the solution for the drift velocity is known [13,21]:…”

Section: Symmetry Propertiesmentioning

confidence: 99%

“…Note that even if the potentials V a (x) and V b (x) alone are symmetric, their average, u(x), can be asymmetric, which results in a nonzero drift velocity (a simple example is given in Ref. [21]). On the other hand, both V a (x) and V b (x) can be asymmetric, but nevertheless A = 0 as this occurs in the case where…”

Section: Symmetry Propertiesmentioning

confidence: 99%

Adiabatically slow and adiabatically fast driven ratchets

et al. 2012

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We revisit two known models of deterministically driven ratchets, which exhibit high energetic efficiency, with the goal to uncover similarities and differences in the principles of their operation. Both the models rely on adiabaticity of the potential change process, however, the adiabaticity that we deal with in the two cases is of different types, slow and fast. It is shown that in the former (latter) case the drift velocity is an even (odd) functional of the potential, with the notable consequence that for the adiabatically slow driven ratchet the necessary symmetry breaking occurs only due to time-dependent parametric perturbations, while the spatial asymmetry of the potential is a mandatory condition for the adiabatically fast driven ratchet to operate. To treat energetic characteristics, the models are restated in terms of traveling potential ratchets. With such an approach, we find that in these cases (i) the conditions of high energetic efficiency to be reached are similar, and (ii) the symmetry properties of the kinetic coefficients are different. Based on our results, a strategy for designing efficient Brownian motors is suggested.

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“…Two main paradigms are recognized in this concept: flashing ratchets [16][17][18] in which transported particles are exposed to a time-fluctuating binding potential along their periodic track, and rocking ratchets [19][20][21] in which the particles move in an asymmetric periodic potential under the action of a spatially uniform time-dependent zero-mean force. The properties of the two ratchet types essentially differ in the adiabatic limit and are characterized by the various mechanisms of current reversal [22,23].…”

Section: Introductionmentioning

confidence: 99%

Two-state Brownian motor driven by synchronously fluctuating unbiased forces

Розенбаум

Makhnovskii

Sheu³

et al. 2011

Phys. Rev. E

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As a model of the Brownian motor, we consider a particle moving unidirectionally under the action of two synchronously fluctuating unbiased forces, transverse and longitudinal with respect to the particle track. The former force induces track-normal transitions of the particle between the attached and detached states (with and without a periodic potential, respectively), whereas the latter drives track-parallel motion in either state. Analytical expressions of the current and efficiency are derived for different regimes, with due account of the delayed response of the system to force fluctuations. For a sawtooth potential in the attached state, we reveal several motion regimes affording the maximum current or the maximum efficiency. A special emphasis is placed on the possibility of current reversal. As shown, the interplay between two phase-shifted harmonically varied forces as well as inherent and externally induced asymmetry can lead to the emergence of multiple current reversals, thus enabling the flexible controllability of the motion direction.

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Brownian motor with competing spatial and temporal asymmetry of potential energy

Cited by 38 publications

References 34 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

Adiabatically slow and adiabatically fast driven ratchets

Two-state Brownian motor driven by synchronously fluctuating unbiased forces

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