ac-driven Brownian motors: a Fokker-Planck treatment

TL;DR

This paper presents a Fokker-Planck equation approach to analyze ac-driven Brownian motors, enabling efficient computation of ratchet transport properties by transforming stochastic dynamics into linear algebra problems.

Contribution

It introduces a Fokker-Planck method for studying ac-driven Brownian motors, providing a deterministic alternative to stochastic simulations and facilitating further generalizations.

Findings

Complete characterization of ratchet transport achieved.

Avoids long transients and statistical fluctuations of stochastic methods.

Framework applicable to various dynamical ratchet systems.

Abstract

We consider a primary model of ac-driven Brownian motors, i.e., a classical particle placed in a spatial-time periodic potential and coupled to a heat bath. The effects of fluctuations and dissipations are studied by a time-dependent Fokker-Planck equation. The approach allows us to map the original stochastic problem onto a system of ordinary linear algebraic equations. The solution of the system provides complete information about ratchet transport, avoiding such disadvantages of direct stochastic calculations as long transients and large statistical fluctuations. The Fokker-Planck approach to dynamical ratchets is instructive and opens the space for further generalizations.