The exact life time of the metastable state
in the tilted cosinusoidal potential profile
A.N. Malakhov, A.L. Pankratov
Radiophysical Dept.,
Nizhny Novgorod State University,
Nizhny Novgorod, Russia
The surmounting of a potential energy barrier by a particle undergoing Brownian motion plays a significant role in a wide variety of a physical, chemical and biological processes, and the prediction of a barrier crossing temporal scales is therefore a problem of considerable theoretical and practical importance.
This work is concerned with the one-dimensional Brownian motion in the polystable system described by the tilted cosinusoidal potential profile: u(x)=1-cosx-ax, where x is the dimensionless coordinate and a is an arbitrary parameter (a;SPMgt;0). Using a new general procedure of obtaining time characteristics of nonstationary diffusion the exact life time of the metastable state was obtained. This expression has been analyzed and disscussed. In particular, in the case when a;SPMlt;1 and fluctuations intensity is small our formula coincides with Kramers' formula [1]. For the case when a;SPMgt;1 and fluctuations intensity is equal to zero, our formula coincides with another one, obtained in paper [2]. Applications of obtained results to problems in Josephson electronics are considered also.