The stochastic pump current and the non-adiabatic geometrical phase

Abstract

We calculate a pump current in a classical two-state stochastic chemical kinetics bymeans of the non-adiabatic geometrical phase interpretation. The two-state systemis attached to two particle reservoirs, and under a periodic perturbation of thekinetic rates, it gives rise to a pump current between the two-state system and theabsorbing states. In order to calculate the pump current, the Floquet theoryfor the non-adiabatic geometrical phase is extended from a Hermitian case to anon-Hermitian case. The dependence of the pump current on the frequency of theperturbative kinetic rates is explicitly derived, and a stochastic resonance-like behavior isobtained.