Quantum Brownian motion in ratchet potentials: duality relation and its consequences

TL;DR

This paper explores quantum Brownian motion in ratchet potentials using a duality relation, connecting long-time dynamics with a driven tight-binding model, and derives a simple expression for the ratchet current.

Contribution

It introduces a duality relation that links quantum Brownian motion in ratchet potentials to a driven tight-binding model, providing new analytical tools.

Findings

Derived a simple expression for ratchet current

Established a duality relation linking two quantum systems

Provided insights into long-time dynamics in dissipative quantum systems

Abstract

Quantum Brownian motion in ratchet potentials is investigated by means of an approach based on a duality relation. This relation links the long-time dynamics in a tilted ratchet potential in the presence of dissipation with the one in a driven dissipative tight-binding model. The application to quantum ratchet yields a simple expression for the ratchet current in terms of the transition rates in the tight-binding system.