Low-temperature quantum fluctuations in overdamped ratchets

TL;DR

This paper investigates how quantum fluctuations influence directed transport in overdamped ratchets at low temperatures, revealing complex behaviors of quantum corrections and providing methods for consistent numerical analysis.

Contribution

It systematically analyzes higher-order quantum corrections in overdamped ratchets and demonstrates their non-trivial effects on transport properties.

Findings

Higher-order quantum contributions can reverse current directions.

Quantum corrections exhibit non-monotonous behavior.

The study offers a consistent approach for numerical simulations of overdamped quantum systems.

Abstract

At low temperatures and strong friction the time evolution of the density distribution in position follows a quantum Smoluchowski equation. Recently, also higher-order contributions of quantum fluctuations to drift and diffusion coefficients have been systematically derived. As a non-trivial situation to reveal the impact of subleading quantum corrections and to demonstrate convergence properties of the perturbation series, directed transport in ratchets is studied. It is shown that the perturbation series typically has a non-monotonous behavior. Depending on symmetry properties higher order contributions may even compensate current reversals induced by leading quantum fluctuations. This analysis demonstrates how to consistently treat the dynamics of overdamped quantum systems at low temperatures also in numerical applications.