Decoherence of a particle in a ring

TL;DR

This paper derives a perturbative formula for dephasing rates of a particle in a ring interacting with an environment, revealing temperature-dependent behavior and implications for quantum coherence.

Contribution

It introduces a new perturbative approach to quantify dephasing in a particle-environment system, specifically applied to a particle on a ring in a dirty metal environment.

Findings

Dephasing rate scales as T^{3/2} at low temperatures.

Identifies dephasing lengths for different ring sizes.

Zero temperature coherence is suppressed by spatial fluctuations.

Abstract

We consider a particle coupled to a dissipative environment and derive a perturbative formula for the dephasing rate based on the purity of the reduced probability matrix. We apply this formula to the problem of a particle on a ring, that interacts with a dirty metal environment. At low but finite temperatures we find a dephasing rate $\propto T^{3/2}$, and identify dephasing lengths for large and for small rings. These findings shed light on recent Monte Carlo data regarding the effective mass of the particle. At zero temperature we find that spatial fluctuations suppress the possibility of having a power law decay of coherence.