The stochastic pump current and the non-adiabatic geometrical phase

2007/12/31 by Jun Ohkubo · 2 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Current (fluid) #Floquet theory #Hermitian matrix #Kinetic energy #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Phase (matter) #Quantum many-body systems #cond-mat.stat-mech #physics.bio-ph #stochastic dynamics and bifurcation

paper · pdf · doi:10.1088/1742-5468/2008/02/p02011

published as J. Stat. Mech. P02011 (2008) · 11 pages

openalex publication_date 2008/02/26 · arxiv created 2008/02/29 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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.

Citations

• Solution of the Schrödinger Equation with a Hamiltonian Periodic in Time
• Stochastic gene expression as a many-body problem

Cited by

• Pumping Restriction Theorem for Stochastic Networks
• Noncyclic and nonadiabatic geometric phase for counting statistics