Current and fluctuation in a two-state stochastic system under non-adiabatic periodic perturbation

TL;DR

This paper investigates the current and its fluctuations in a two-state stochastic system under non-adiabatic periodic perturbation, revealing resonance-like behavior in the average current but not in its fluctuation, using geometrical phase and Floquet theory.

Contribution

It introduces a simple calculation scheme for current statistics in non-adiabatic regimes based on geometrical phase and Floquet theory.

Findings

Average current exhibits stochastic-resonance-like behavior.

Current fluctuation does not show resonance-like behavior.

Provides a practical calculation recipe for non-adiabatic current statistics.

Abstract

We calculate a current and its fluctuation in a two-state stochastic system under a periodic perturbation. The system could be interpreted as a channel on a cell surface or a single Michaelis-Menten catalyzing enzyme. It has been shown that the periodic perturbation induces so-called pump current, and the pump current and its fluctuation are calculated with the aid of the geometrical phase interpretation. We give a simple calculation recipe for the statistics of the current, especially in a non-adiabatic case. The calculation scheme is based on the non-adiabatic geometrical phase interpretation. Using the Floquet theory, the total current and its fluctuation are calculated, and it is revealed that the average of the current shows a stochastic-resonance-like behavior. In contrast, the fluctuation of the current does not show such behavior.