Diffusion of particles subject to nonlinear friction and a colored noise

Abstract

Stochastic motion with nonlinear friction has several applications in physics and biology. For only a few cases, expressions for the diffusion coefficient with nonlinear friction and white Gaussian noise have been derived. Here I study one-dimensional nonlinear velocity dynamics driven by exponentially correlated ('colored') noise. For the case of a dichotomous colored noise, I calculate an exact quadrature expression for the diffusion coefficient of the resulting motion for a general odd friction function and evaluate it for three different friction functions: a pure cubic friction, a quintic friction and the Rayleigh-Helmholtz (RH) friction function. For quintic friction as well as for RH friction, the diffusion coefficient attains a minimum at a finite correlation time of the dichotomous noise. The very same effect is seen in numerical simulations with an Ornstein-Uhlenbeck process (OUP) instead of a discrete noise. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.