Duality Relation for Quantum Ratchets

TL;DR

This paper establishes a duality relation linking the dynamics of quantum Brownian particles in ratchet potentials to driven tight-binding models, revealing insights into transport, rectification, and current reversals.

Contribution

It introduces a novel duality relation connecting weak and strong dissipation regimes in quantum ratchet systems, enabling new analysis of their transport properties.

Findings

Ground-state delocalization inferred from linear mobility.

Reversals in ratchet current induced by adiabatic driving and temperature.

Dependence of current behavior on potential shape.

Abstract

A duality relation between the long-time dynamics of a quantum Brownian particle in a tilted ratchet potential and a driven dissipative tight-binding model is reported. It relates a situation of weak dissipation in one model to strong dissipation in the other one, and vice versa. We apply this duality relation to investigate transport and rectification in ratchet potentials: From the linear mobility we infer ground-state delocalization for weak dissipation. We report reversals induced by adiabatic driving and temperature in the ratchet current and its dependence on the potential shape.