Interference in presence of Dissipation

TL;DR

This paper investigates how dissipation affects quantum interference in a particle on a ring, developing a variational and RG approach to understand the decay of Aharonov-Bohm oscillations under different environments.

Contribution

It introduces a variational scheme combined with an all-orders RG analysis to study dissipation effects on quantum interference in ring systems.

Findings

AB oscillation amplitude decays exponentially with R^2 in certain environments

Dissipation from a metal induces a R^{-2} decay of AB amplitude for large R

Cold atoms with electric dipoles may exhibit a crossover between behaviors

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. We analyze our solution within a renormalization group (RG) scheme to all orders which reproduces a 2 loop RG for the Caldeira-Legget environment. In the latter case the Aharonov-Bohm (AB) oscillation amplitude is exponential in -R^2 where R is the ring's radius. For either a charge or an electric dipole coupled to a dirty metal we find that the metal induces dissipation, however the AB amplitude is ~ R^{-2} for large R, as for free particles. Cold atoms with a large electric dipole may show a crossover between these two behaviors.