A generalizad Fokker-Planck equation for the ratchet problem: Memory effects

TL;DR

This paper develops a generalized Fokker-Planck equation incorporating memory effects to analyze stochastic ratchets with inertia, revealing feedback-induced instabilities and illustrating stochastic resonance phenomena.

Contribution

The paper introduces a novel Fokker-Planck framework that includes memory effects for the ratchet problem, validated against Langevin simulations.

Findings

Memory effects significantly influence ratchet dynamics.

Positive feedback leads to instabilities in the system.

Memory can induce stochastic resonance-like behavior.

Abstract

We study stochastic ratchets with inertia in the limit where the time correlations become important. We have developed a Fokker-Planck type equation for the ratchet problem which includes the memory effects. It is tested with comparison to the Langevin simulations. The effect of the memory in the system is analyzed extensively. A positive feedback regime which manifests itself as instabilities is observed. This may be regarded as an illustration of stochastic resonance.