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.
Kulikov, D.A., Agudov, N.V., Spagnolo, B. (2011). Gaussian models for the distribution of Brownian particles in tilted periodic potentials. THE EUROPEAN PHYSICAL JOURNAL. B, CONDENSED MATTER PHYSICS, 83(2), 263-269 [10.1140/epjb/e2011-20372-x].
Gaussian models for the distribution of Brownian particles in tilted periodic potentials
SPAGNOLO, Bernardo
2011-01-01
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.
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