Reaction rate kernel for dichotomous noise-induced transitions in bistable systems

We present a study of the kinetics of transitions between two stochastic states induced by external dichotomous noise in deterministic bistable one-variable systems. The time dependence of the rate kernel describing the transition is studied by relating the kernel to the spectrum of the stochastic dynamical operator projected onto fast time scales. The formalism is applied to an exactly solvable case (the piecewise quadratic potential) and numerically to a quartic potential. This analysis is useful for the study of memory effects in fast reaction rate processes.