The stochastic pump current and the non-adiabatic geometrical phase

TL;DR

This paper investigates the pump current in a classical two-state stochastic system using non-adiabatic geometrical phase theory, extending Floquet analysis to non-Hermitian cases, revealing frequency-dependent behaviors and stochastic resonance phenomena.

Contribution

It introduces a non-adiabatic geometrical phase approach to calculate pump currents in non-Hermitian stochastic systems, extending Floquet theory to this context.

Findings

Pump current depends explicitly on the frequency of kinetic rate perturbations.

A stochastic resonance-like behavior is observed in the pump current.

Theoretical extension of Floquet theory to non-Hermitian systems is achieved.

Abstract

We calculate a pump current in a classical two-state stochastic chemical kinetics by means of the non-adiabatic geometrical phase interpretation. The two-state system is attached to two particle reservoirs, and under a periodic perturbation of the kinetic rates, it gives rise to a pump current between the two-state system and the absorbing states. In order to calculate the pump current, the Floquet theory for the non-adiabatic geometrical phase is extended from a Hermitian case to a non-Hermitian case. The dependence of the pump current on the frequency of the perturbative kinetic rates is explicitly derived, and a stochastic resonance-like behavior is obtained.