Barrier crossing and transport activated by kangaroo fluctuations

Abstract

We study barrier crossing of Brownian particles in a bistable symmetric potential and transport of Brownian particles in spatially periodic structures, driven by both kangaroo fluctuations and thermal equilibrium noise of zero mean values. We consider exponentially and algebraically correlated kangaroo fluctuations. Starting with the full Newton-Langevin equation for the Brownian particle and by introducing scaling as well as dimensionless variables, we show that the equation is very well approximated by overdamped dynamics in which inertial effects can be neglected. We analyze properties of selected macroscopic characteristics of the system such as the mean first passage time (MFPT) of particles from one minimum of the bistable potential to the other and mean stationary velocity of particles moving in a spatially periodic potential. In dependence upon statistics of kangaroo fluctuations and temperature of the system, macroscopic characteristics exhibit distinctive non-monotonic behavior. Accordingly, there exist optimal statistics of fluctuations optimizing macroscopic characteristics.