Output velocity distribution of a Langevin system with random binary input

Abstract

The Langevin equation of a particle is considered for one-dimensional motion through a viscous fluid, subject to a stochastic external force modelled by a random binary telegraph signal. For resistance proportional to velocity, a value of the mean binary switching rate is deduced, above which the steady-state particle velocity distribution is effectively gaussian. For resistance proportional to velocity squared, however, it is shown that the velocity distribution does not tend to a gaussian limit however high the switching rate. This latter case provides a simple illustration of a noise-induced phase transition in a non-linear system.