Dissipative corrections to escape probabilities of thermal-nonequilibrium systems

Abstract

Dissipative corrections to the logarithm of the probability of escape from a metastable state of an underdamped Markov system are considered. The approach proposed is based on the Poincaré cross-section method applied to the optimal path along which a system moves, with an overwhelming probability, in the course of a fluctuation resulting in escape. The corrections depend crucially on the structure of the trajectories of motion of the system near the saddle point in the absence of dissipation and fluctuations. For two important patterns of the trajectories the corrections are ∼${\mathrm{\eta }}^2$ lnη and ∼η, where η is a dissipation parameter. Numerical analysis of the escape probabilities for a nonlinear oscillator bistable in a nearly resonant field is fulfilled and the results are shown to be in good agreement with the analytical predictions. A new feature of the pattern of the optimal paths in systems without detailed balance, the onset of caustics, is revealed.