Time behaviour of non-linear stochastic processes in the presence of multiplicative noise: From Kramers' to Suzuki's decay

Abstract

The diffusional regime of a Brownian particle in a double-well potential in the presence of both additive and multiplicative noise is explored. As a relevant effect of the multiplicative noise, the escape rate from a well is shown to change from the small value of the Kramers theory into the large relaxation rate of the Suzuki regime. It is shown, furthermore, that the time required to get equilibrium in a well after sudden application of multiplicative noise (the activation time) is very much shorter than the Kramers relaxation time. We envisage therefore an operational scheme making available multiplicative noise for a short interval of time (for example using a light pulse) as an efficient tool to get a fast process of escape from a well. These results are obtained by using a continued-fraction algorithm which makes it possible even to successfully deal with the decay of an unstable state at the critical point.