Some stochastic phenomena in a driven double-well system

TL;DR

This paper investigates stochastic phenomena such as hysteresis, stochastic resonance, and unidirectional motion in a driven double-well system, revealing their interrelations and the role of noise in these processes.

Contribution

It introduces a new measure of synchronization based on hysteresis loop area and explores noise-induced stability effects in large amplitude driving fields.

Findings

Hysteresis loop area correlates with synchronization of well passages.

Stochastic resonance persists even with large amplitude driving fields.

Noise can stabilize unstable states, affecting system dynamics.

Abstract

We study the overdamped motion of a Brownian particle in a driven double-well system to understand various physical phenomena observed experimentally. These phenomena include hysteresis, stochastic resonance, and net unidirectional motion in a symmetric periodic system. We argue that the area of the hysteresis loop so defined is a good measure of synchronization (with respect to the applied field) of passages between the two wells. We find that stochastic resonance may be relevant even in case of large amplitude driving field due to a recently discovered phenomena of noise induced stability of unstable states. We try to find relation between some of these apparently different phenomena.