Optimization of Brownian Transport in a System of Globally Coupled Phase Oscillators by Means of Colored Noise

Abstract

In a previous work^[1], we performed a mean-field analysis of a model for noise-induced transport (“ratchet” behavior)^[2]: a system of nonlinear phase oscillators—globally coupled with strength K ₀ and submitted to local “flashing” potentials with common noise strength Q— undergoes a reentrant noise-induced non-equilibrium phase transition towards a brokensymmetry phase characterized by an asymmetric stationary mean-field probability distribution function (PDF) p ^st(x), and exhibiting a spontaneous particle current ($\left\langle {\dot X} \right\rangle \ne 0$ in the absence of a load force F) and hysteresis in its $\left\langle {\dot X} \right\rangle$ vs F characteristic. Our focus was the relationship between the (normal or anomalous) character of the hysteresis loop, the number of “homogeneous” mean-field solutions, and the shape of p ^st(x). In subsequent works^[3] we let the multiplicative noises that drive the “flashing” potentials be Ornstein- Uhlenbeck—with common self-correlation time τíand explored the consequences of this assumption on the (Q,K ₀) phase diagram and on the transport properties, resorting to the “unified colored noise approximation” (UCNA). In this work we take a closer look to the efficiency ∈ of the mechanical rectification process (in the region where it is positive) to show that it attains a maximum for a finite value of τ. We also follow the τ-evolution of the shape of the “effective potential” at two points in the phase diagram.