Eur. Phys. J. B 83, 263-269 (2011)
https://doi.org/10.1140/epjb/e2011-20372-x

Gaussian models for the distribution of Brownian particles in tilted periodic potentials

The limit of high barriers

¹ Radiophysics Department, Nizhni Novgorod State University, Nizhni Novgorod, Russia
² Dipartimento di Fisica, Group of Interdisciplinary Physics and CNISM, Università di Palermo, Viale delle Scienze pad. 18, 90128 Palermo, Italy

Corresponding author: ^a bernardo.spagnolo@unipa.it

Received: 15 May 2011
Revised: 11 August 2011
Published online: 23 September 2011

Abstract

We present two Gaussian approximations for the time-dependent probability density function (PDF) of an overdamped Brownian particle moving in a tilted periodic potential. We assume high potential barriers in comparison with the noise intensity. The accuracy of the proposed approximated expressions for the time-dependent PDF is checked with numerical simulations of the Langevin dynamics. We found a quite good agreement between theoretical and numerical results at all times.