Quenching problem of globally coupled bistable stochastic systems with finite size

The transient process of globally coupled bistable systems from an unstable state to metastable state (i.e, quenching process) is studied analytically for small noise intensity. The influences of noise intensity and system size on the system evolution are investigated. The problem of a large number of coupled Langevin equations is reduced to a simple problem of a one-dimensional ordinary differential equation, subject to a white noise with intensity explicitly given. The analytical results are fully confirmed by direct numerical computations.