Asymmetric motion in a double-well under the action of zero-mean Gaussian white noise and periodic forcing

TL;DR

This study investigates how zero-mean asymmetric periodic forcing influences particle residence times in a double-well system under Gaussian white noise, revealing optimal noise levels for maximum asymmetry effects and synchronization.

Contribution

It introduces a numerical analysis of asymmetric periodic forcing effects on residence times and synchronization in a double-well system, highlighting the role of noise strength and asymmetry.

Findings

Residence time differences vary monotonically with forcing asymmetry.

Maximum asymmetry occurs at an optimal noise level.

Asymmetry affects synchronization of well-to-well passages.

Abstract

Residence times of a particle in both the wells of a double-well system, under the action of zero-mean Gaussian white noise and zero-averaged but temporally asymmetric periodic forcings, are recorded in a numerical simulation. The difference between the relative mean residence times in the two wells shows monotonic variation as a function of asymmetry in the periodic forcing and for a given asymmetry the difference becomes largest at an optimum value of the noise strength. Moreover, the passages from one well to the other become less synchronous at small noise strength as the asymmetry parameter (defined below) differs from zero, but at relatively larger noise strengths the passages become more synchronous with asymmetry in the field sweep. We propose that asymmetric periodic forcing (with zero mean) could provide a simple but sensible physical model for unidirectional motion in a symmetric periodic system aided by a symmetric Gaussian white noise.