Transition from anomalous to normal hysteresis in a system of coupled Brownian motors: A mean-field approach

Abstract

We address a recently introduced model describing a system of periodically coupled nonlinear phase oscillators submitted to multiplicative white noises, wherein a ratchetlike transport mechanism arises through a symmetry-breaking noise-induced nonequilibrium phase transition. Numerical simulations of this system reveal amazing novel features such as negative zero-bias conductance and anomalous hysteresis, explained by performing a strong-coupling analysis in the thermodynamic limit. Using an explicit mean-field approximation, we explore the whole ordered phase finding a transition from anomalous to normal hysteresis inside this phase, estimating its locus, and identifying (within this scheme) a mechanism whereby it takes place.

Disordering effects of colour in a system of coupled Brownian motors: phase diagram and anomalous to normal hysteresis transition

“…In Refs. [4,6] it is V (x) = W (x) = − cos x−A cos 2x, hence L = 2π. With the choice A > 0, the direction of the particle current Ẋ turns out to be opposite to that of symmetry breaking in the SPDF P st (x): it is this effect which leads in turn to such oddities as negative zero-bias conductance and anomalous hysteresis [4].…”

“…Although plausibility arguments, detailed in Ref. [6], allow to have an intuition on the existence of some solutions to this integral equation (and their stability) in this symmetric case, the stability of the true solutions must be explicitly checked. Since cos x in Eq.…”

“…NUMERICAL RESULTS for τ = 0 [4,6]). The novelty is that for any τ = 0, the phase transition is also reentrant as a function of K 0 for Q = const (a feature found in Ref.…”

“…Hence in this work, and as a natural continuation to Ref. [6], we study (in mean-field approximation) the consequences of a finite correlation time τ of the multiplicative noises in the model of Refs. [4,6].…”

“…[6], we study (in mean-field approximation) the consequences of a finite correlation time τ of the multiplicative noises in the model of Refs. [4,6]. In the following sections we briefly describe the model and its mean-field treatment, and discuss our numerical results regarding the influence of colour on the phase diagram and on the transition from anomalous to normal hysteresis inside the ordered phase.…”