Current reversals in a rocking ratchet: Dynamical versus symmetry-breaking mechanisms

Abstract

Directed transport in ratchets is determined by symmetry breaking in a system out of equilibrium. A hallmark of rocking ratchets is current reversals: an increase in the rocking force changes the direction of the current. In this work for a biharmonically driven spatially symmetric rocking ratchet we show that a class of current reversal is precisely determined by symmetry breaking, thus creating a link between dynamical and symmetry-breaking mechanisms. Many processes in physics, chemistry, and biology involve directed transport through periodic structures. For the equilibrium situation of Brownian motion, diffusion can be turned into directed diffusion by the application of a dc bias. In out-of-equilibrium systems, new mechanisms for directed transport may arise. Counterintuitively, far from equilibrium it is possible to obtain directed transport through a macroscopically flat potential in the absence of an applied dc bias. This is the so-called ratchet effect ͓1-7͔.The archetypal of a ratchet device is the rocking ratchet. In this setup, Brownian particles experience an asymmetric sawtooth potential and a sinusoidal rocking force. The rocking force drives the system out of equilibrium, and directed transport is generated following the breaking of the symmetries of the system. An analogous effect can also be produced in a spatially symmetric potential and a biharmonic force, with the latter playing the double role of driving the system out of equilibrium and breaking the relevant time symmetries ͓8-16͔.A hallmark of rocking ratchets is current reversals. By progressively increasing the rocking force from zero, the generation of a current is observed, whose magnitude is first an increasing function of the strength of the driving. However, at larger values of the rocking force the current reaches a maximum, then decreases to zero, and changes sign. This feature can appear several times in a given system for different values of the force, thus producing multiple current reversals. Single and multiple current reversals have been observed in a variety of systems, both for an asymmetric potential and a symmetric drive and for a symmetric potential and a time-asymmetric drive ͓17-19͔.Current reversals are usually considered a dynamical effect, not related to the symmetry breaking required to allow directed motion. In this work, for the specific system with a spatially symmetric potential and a time-asymmetric drive, we show that a class of current reversal is actually determined by dissipation-induced symmetry breaking. As a consequence, these reversals are not present in the Hamiltonian limit or in the overdamped limit.Our work consists of a theoretical analysis of the relationship between current reversals and dissipation-induced symmetry breaking. This is carried out comparing differing regimes: weakly damped, Hamiltonian, and overdamped. In the case of weak damping, where current reversals associated with dissipative effects are present, the theoretical analysis is also supported by experimental results obtained ...

Current reversals in a rocking ratchet: The frequency domain

“…This generalizes the link between symmetry breaking and current reversals established in Ref. [16] in the case of current reversals in the amplitude domain. Fig.…”

“…[16], and we recall here only the essential elements. Up to 10 8 87 Rb atoms are trapped and cooled down to ∼50 μK in a magneto-optical trap.…”

“…A different approach toward understanding current reversals induced by a variation of the rocking force amplitude was recently introduced for a biharmonically driven, spatially symmetric rocking ratchet [16]. It was shown that a class of current reversals is precisely determined by symmetry breaking.…”

Multiple Current Reversals Using Superimposed Driven Lattices

“…In contrast to Brownian ratchets, our mechanism does not depend on noise and operates in the purely Hamiltonian regime. The effect of weak noise typical for ratchet experiments with cold atoms and underdamped colloids [10,58] represent minor fluctuations of the average velocity of the ensemble and this does not affect the functionality of the current reversal mechanism. Interaction and disorder have been shown to enhance accumulation of particles within the regular regions of the phase space [33,59,60], which would aid the conversion of chaotic to ballistic dynamics of particles.…”

Freezing, accelerating, and slowing directed currents in real time with superimposed driven lattices

“…This can have important consequences for the transport [37], but it affects the particle distribution in phase space only on long timescales [37] and should therefore leave our scheme unaffected. In contrast to Brownian ratchets, our mechanism does not depend on noise and we explicitly checked that it is robust to noise of strengths in the regime typical for cold atom ratchet experiments [38]. Stronger noise would enhance the particle flux through the cantori and other regular structures significantly decreasing both the maximally achievable transport velocity and the operational timescale of our scheme.…”