Transient response of a Brownian particle with general damping

We study the transient response of a Brownian particle with general damping in a system of metastable potential well. The escape rate is evaluated as a function of time after an infinite wall is removed from the potential barrier. It takes a relaxation time for the rate to reach its limit value and this rate relaxation time differs from the relaxation time of the majority of the probability around the bottom of the potential well. The rate relaxation time is found to depend on the temperature as well as the damping constant. It involves the diffusion time and the instanton time, in general agreement with recent studies of the overdamped case by Bier et al. Phys. Rev. E 59, 6422 (1999)].