Non-Markov noise in barrier-fluctuation model

Abstract

We investigate the thermally activated escape of a particle over a potential barrier whose height fluctuates between two values. The barrier-switching process is constructed as a semi-Markov alternating process: the times at which a change of the barrier state can occcur form a general renewal process and the probability of leaving a state depends on the time the barrier resides in the state before the jump. During the interjump interval, the barrier is fixed in one of the two states and the crossing dynamics is described by a general (not necessarily exponential) decay law. We give the general formulae describing the averaged escape dynamics, where the averaging runs over all possible histories of the switching process. Using the above device of the selective residence times, the recently discussed phenomenon of resonant activation (a minimal averaged lifetime of the particle in the potential well) emerges also within the framework of the conventional exponential escape dynamics.