Relaxation in a Bistable System

Abstract

A double-Gaussian approximation method is introduced to treat the relaxation process in a bistable system with two stable and one unstable states: An initial single-peak distribution is assured to relax to the equilibrium double-peak distribution in a cooperative macro-system. If the initial peak stays far from the unstable point, the logarithm of the relaxation time for the appearance of double-peak is very long and proportional to the size N of the system: The single-peak distribution is metastable. If the initial peak stays at the unstable point, the relaxation time is proportional to log N. In this case, further, fluctuation increases anomalously to the order of unity in the intermediate stage.