The Aharonov-Bohm effect in presence of dissipative environments

TL;DR

This paper investigates how dissipative environments affect a particle on a ring, developing a variational RG approach that reproduces known results and reveals a weak dissipation regime with specific decay behavior.

Contribution

It introduces a variational scheme and RG analysis for a particle on a ring with dissipation, extending to all orders and reproducing two-loop results.

Findings

RG transformation to all orders in inverse dissipation strength

Reproduction of known two-loop results

Identification of a weak dissipation regime with 1/t^2 decay in imaginary time

Abstract

We study a particle on a ring in presence of various dissipative environments. We develop and solve a variational scheme assuming low frequency dominance. Our solution produces a renormalization group (RG) transformation to all orders in the inverse dissipation strength, and in particular reproduces known two loop results. Our RG leads to a weak dissipation parameter, for which a weak coupling expansion for the position correlation function shows a 1/t^2 decay in imaginary time.