Ratchet effect on a relativistic particle driven by external forces

Quintero, Niurka R.; Álvarez-Nodarse, R.; Cuesta, José A.

doi:10.1088/1751-8113/44/42/425205

Cited by 8 publications

(10 citation statements)

References 38 publications

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“…If the system satisfies certain symmetries, the theory predicts that the phase lags can no longer be modified by changing the amplitudes of the harmonics (Corollary 2). This is indeed what happens in some equations for particles or solitons moving in a nonlinear potential and in certain experiments [23,25,29,41].…”

Section: Discussionsupporting

confidence: 60%

“…That this is not the case has been shown in experiments [39], simulations [11,40], and also theoretically in Ref. [41]. The application of this method apparently captures the right dependence on the amplitudes in the case of harmonic mixing, but this is purely accidental.…”

Section: Introductionmentioning

confidence: 82%

“…(For an in-depth analysis of this method and its many flaws, see Refs. [38,41] and references therein. )…”

Section: Introductionmentioning

confidence: 99%

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Time-Shift Invariance Determines the Functional Shape of the Current in Dissipative Rocking Ratchets

2013

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Ratchets are devices able to rectify an otherwise oscillatory behavior by exploiting an asymmetry of the system. In rocking ratchets the asymmetry is induced through a proper choice of external forces and modulations of nonlinear symmetric potentials. The ratchet currents thus obtained in systems as different as semiconductors, Josephson junctions, optical lattices, or ferrofluids, show a set of universal features. A satisfactory explanation for them has challenged theorist for decades, and so far we still lack a general theory of this phenomenon. Here we provide such a theory by exploring -through functional analysis-the constraints that the simple assumption of time-shift invariance of the ratchet current imposes on its dependence on the external drivings. Because the derivation is based on so general a principle, the resulting expression is valid irrespective of the details and the nature of the physical systems to which it is applied, and of whether they are classical, quantum, or stochastic. The theory also explains deviations observed from universality under special conditions, and allows us to make predictions of phenomena not yet observed in any experiment or simulation.

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Section: Discussionsupporting

confidence: 60%

Section: Introductionmentioning

confidence: 82%

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Time-Shift Invariance Determines the Functional Shape of the Current in Dissipative Rocking Ratchets

2013

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“…On the other hand, large damping strongly reduces the mobility. As a consequence, transport is maximized for intermediate values of damping [38]. The CC approach (red dashed line) suitable describes this non-monotonous behaviour and the location of the peak.…”

Section: Numerical Studymentioning

confidence: 94%

Collective coordinates theory for discrete soliton ratchets in the sine-Gordon model

et al. 2014

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A collective coordinate theory is developed for soliton ratchets in the damped discrete sine-Gordon model driven by a biharmonic force. An ansatz with two collective coordinates, namely the center and the width of the soliton, is assumed as an approximated solution of the discrete nonlinear equation. The dynamical equations of these two collective coordinates, obtained by means of the generalized travelling wave method, explain the mechanism underlying the soliton ratchet and capture qualitatively all the main features of this phenomenon. The numerical simulation of these equations accounts for the existence of a nonzero depinning threshold, the nonsinusoidal behavior of the average velocity as a function of the relative phase between the harmonics of the driver, the nonmonotonic dependence of the average velocity on the damping, and the existence of nontransporting regimes beyond the depinning threshold. In particular, it provides a good description of the intriguing and complex pattern of subspaces corresponding to different dynamical regimes in parameter space.

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“…The mechanism responsible for the appearance of a directed motion caused by a zero-mean force has been well understood for particles moving in spatial periodic potentials, such as particle separating devices [18] and relativistic particles [19]. Relatively recently ratchet dynamics has been shown to exist for quasiparticles, such as solitons and large polarons [6][7][8][9][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Thermal enhancement and stochastic resonance of polaron ratchets

et al. 2014

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. (2014) 'Thermal enhancement and stochastic resonance of polaron ratchet.', Physical review E., 89 (6). 062905.Further information on publisher's website:http://dx.doi.org/10.1103/PhysRevE.89.062905Publisher's copyright statement:Reprinted with permission from the American Physical Society: L. S. Brizhik, A. A. Eremko, B. M. A. G. Piette, and W. J. Zakrzewski, Physical Review E, 89, 062905, 2014. c 2014 by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modied, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society. Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. We study the ratchet drift of large polarons (solitons) in molecular diatomic chains induced by unbiased time periodic electric fields at nonzero temperature below its critical value. We show that, at a nonzero temperature, the critical value of the intensity of the electric field above which the ratchet phenomenon takes place is lower than at zero temperature for the same frequency of the field. We show that there is a range of temperatures for which the polaron drift is larger than that at zero temperature. We also show that temperature decreases the value of the lowest critical period of the field. And, finally, we demonstrate that there is a stochastic resonance in a polaron ratchet, namely that there is an optimal temperature at which the polaron drift is a maximum. The values of the stochastic resonance temperature, the lowest critical values of the field intensity, and its period depend on various parameters of the system and, in particular, on the anisotropy of the chain parameters. This temperature induced decrease of the critical value of the field intensity and its period, as well as the stochastic resonance itself, may be important for practical applications of the ratchet phenomenon in systems involving conducting polymers and other low-dimensional materials. They may also be important in some biological macromolecules where the ratchet phenomenon could take place in biomotors and energy and/or charge transport.

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Ratchet effect on a relativistic particle driven by external forces

Cited by 8 publications

References 38 publications

Time-Shift Invariance Determines the Functional Shape of the Current in Dissipative Rocking Ratchets

Time-Shift Invariance Determines the Functional Shape of the Current in Dissipative Rocking Ratchets

Collective coordinates theory for discrete soliton ratchets in the sine-Gordon model

Thermal enhancement and stochastic resonance of polaron ratchets

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