Passage through a barrier with a slowly increasing control parameter

A bistable system subjected to noise and a slow increase of the parameter c ontrolling the instability is studied, with emphasis on the kinetics of the transitions across the barrier separating the stable states. It is shown t hat the presence of a ramp in the control parameter may considerably affect the distribution of probability mass on the two sides of the barrier as co mpared to the predictions of the classical Kramers theory.