The stochastic pump current and the non-adiabatic geometrical phase

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.

11 pages

References in corpus (4)

• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• The unified geometric theory of mesoscopic stochastic pumps and reversible ratchets
• Driving particle current through narrow channels using classical pump
• A field theoretic approach to master equations and a variational method beyond the Poisson ansatz

Cited by in corpus (5)

• Directed flow in non-adiabatic stochastic pumps
• Pumping-Restriction Theorem for Stochastic Networks
• Particle current in symmetric exclusion process with time-dependent hopping rates
• Geometric phase for non-Hermitian Hamiltonian evolution as anholonomy of a parallel transport along a curve
• Hannay angle and geometric phase shifts under adiabatic parameter changes in classical dissipative systems