Vanishing of first-passage times near the limit of metastability

Abstract

First-passage times T_p for n-variable metastable systems vanish as the control parameter μ approaches its spinodal value μ_c1, with T_p~|μ-μ_c1|^θ_p typically. The barrier height-to-noise ratio is the small parameter. The general results for the exponent θ_p agree with the exactly soluble n=1 case where θ_p=1/2, and are applied to the n=4 two-mode laser, where θ_p=2 is predicted.