Transport and dynamical properties of inertial ratchets

Abstract

In this paper we discuss the dynamics and transport properties of a massive particle, in a time dependent periodic potential of the ratchet type, with a dissipative environment. The directional currents and characteristics of the motion are studied as the specific frictional coefficient varies, finding that the stationary regime is strongly dependent on this parameter. The maximal Lyapunov exponent and the current show large fluctuations and inversions, therefore for some range of the control parameter, this inertial ratchet could originate a mass separation device. Also an exploration of the effect of a random force on the system is performed.Comment: PDF, 16 pages, 7 figure

Deterministic inhomogeneous inertia ratchets

“…[16], has also contributed significantly to the understanding of the subject. These deterministic ratchets, unaided by noise, are shown to yield current in overdamped [17,18], underdamped [14,16,19,20,21,22,23,24,25,27,28], as well as in Hamiltonian [29,30,31] periodic potential systems, and also in overdamped quenched disordered [32,34] systems. In these systems net current results, without the presence of applied nonzero average forcing or asymmetric fluctuations, due to the presence of various regular transporting or chaotic attractors depending on the initial conditions for given system parameter values.…”

“…The transport properties of inertial systems depend sensitively on the (constant) friction parameter [26,27,28]. The addition of noise to the system in the low damping regime makes the system dynamics robust against initial conditions [27].…”

“…In Ref. [28] the effect of noise on individual transporting deterministic trajectories is analysed. A small noise seem to have little effect on some trajectories in one direction whereas it destroys trajectories in the opposite direction resulting in a robust finite ratchet current.…”

“…However, the stroboscopic Poincaré plots differ qualitatively in the driven system as the inhomogeneity parameter λ is varied. Links Vi The presence of noise (which is ubiquitous in natural environments) smooths out the current fluctuations so numerously present in the deterministic case [28,41]. In Ref.…”

Transport properties and current inversion by white Gaussian noise in a coupled ratchet model

“…It is well known that a ratchet system is a set of particles (interacting or not) far from the equilibrium and due to their spatial-temporal symmetries may present a directional current even when the acting forces have zero mean value. They may be classified as deterministic [1], stochastic [2] (Brownian), and inertial [3] (under damped [4] or over damped). From early works, this kind of system [5,6] (for comprehensive reviews see refs in [7] and [8]) have been the object of interest in many fields [9], since it provides not only the understanding of the transport phenomena in biological systems [10][11][12] but has quite an importance in the design and construction of artificial devices (classical or quantum, [13] and the references therein).…”