Lifetime of oscillatory steady states

Abstract

We introduce a method to derive expressions for the distribution $\ensuremath{\rho}$ of large fluctuations about a stable oscillatory steady state and for the transition rate from that state into another stable state. Our method is based on a WKB-type expansion of the solution of the Fokker-Planck equation. The expression for $\ensuremath{\rho}$ has a form similar to the Boltzmann distribution with the energy replaced by a function $W$, which is the solution of a Hamilton-Jacobi-type equation. For the case of small dissipation, a simple analytical approximation to $W$, in terms of an action increment, is derived. Our results are employed to predict various measurable quantities in physical systems. Specifically we consider the problems of the physical pendulum, the shunted Josephson junction, and the transport of charge-density-wave excitations.