Current reversals and synchronization in coupled ratchets

Abstract

Current reversal is an intriguing phenomenon that has been central to recent experimental and theoretical investigations of transport based on ratchet mechanism. By considering a system of two interacting ratchets, we demonstrate how the coupling can be used to control the reversals. In particular, we find that current reversal that exists in a single driven ratchet system can ultimately be eliminated with the presence of a second ratchet. For specific coupling strengths a currentreversal free regime has been detected. Furthermore, in the fully synchronized state characterized by the coupling threshold k th , a specific driving amplitude aopt is found for which the transport is optimum. Transport phenomena and, particularly, directed transport occur in many situations ranging from physical systems to chemical and biological systems. Some recent research interest in transport problems is related to ratchet physics where unbiased, noise-induced transport occurs away from thermal equilibrium as a result of the action of Brownian motors [1][2][3]. Brownian motors, especially "ratchet" models, have been widely investigated partly due to the challenge to describe and control mechanisms of fundamental biological processes at both the cell level (e.g. transport in ion channels) and body level (muscle operations) [4]. Another motivation is derived from recent advances in technology wherein devices for guiding tiny particles on nano/micro scales are sought; these include particle separation techniques, smoothing of atomic surfaces during electromigration and control of the motion of vortices in superconductors [2,5]. Remarkably, experimental realizations of some of these practical systems have been reported [6][7][8].In this framework, two basic types of ratchet models have commonly been employed, namely: (i) the rocking ratchet, in which the particle is subject to an unbiased external force with or without additive noise, and (ii) the flashing ratchet, in which the particle is periodically kicked. The vast majority of these models are overdamped where the noise plays a vital role in the transport process. However, recent studies have shown that the role of noise can be replaced by deterministic chaos induced by the inertial term [9]. In such inertial ratchets, the issue of current reversal has been carefully investigated [10][11][12][13][14]. Moreover, Hamiltonian ratchets have re- * Corresponding author: u.vincent@tu-clausthal.de cently seen a breakthrough in the ratchet community [15]. Here the noise and particularly the dissipation are absent, thereby allowing these systems to preserve their full coherence. Hamitonian ratchets owe their merit to the first experimental realization of the quantum ratchet potential [16,17] which has been a very good motivation for more theoretical as well as experimental works. In this context, higher order quantum resonances (a regime of very fast and directed transport) have been found with atoms [18], and directed transport of atoms has quite recently been experimentally achieved [19]...

Multidimensional washboard ratchet potentials for frustrated two-dimensional Josephson junctions arrays on square lattices

“…For our potential, we conjecture that inertial effects (β c = 0) can produce a dynamical ratchet. Also we expect the current reversal phenomenon to exist in our system [46], in fact our systems are prominent examples of ratchets in which inertia, dissipation and noise combines together with high dimensionality and chaos [34] similar to the theory of molecular motors [36,44][20] [21]. Potentials for symmetric values of f around f = 1/2, for example f = 1/4 and f = 3/4 [23], appear interesting and can also be found with the method.…”

Cooperative surmounting of bottlenecks

“…This study differs from the previous two in that a current reversal is obtained through the appropriate selection of (completely symmetric) initial conditions, rather than through the modification of a control parameter. These studies have been extended to consider the case of two coupled driven and damped particles evolving in a ratchet potential [103]. Not surprisingly, the addition of the second particle can have important consequences for the current reversals observed in the case of the single particle.…”

Deterministic Smoluchowski-Feynman ratchets driven by chaotic noise

“…This has motivated us to examine the behavior of ratchets subjected to chaotic noise. Ratchets driven by chaotic noise are deterministic ratchets [14][15][16][17][18][19][20] because chaotic noise originates from deterministic systems. Since we will be restricting our studies to the overdamped regime, our ratchets belong to the class of overdamped deterministic ratchets [21,22], instead of the inertia [23][24][25] or the Hamiltonian deterministic ratchets [26,27].…”