Received 12 April 2006; revised 3 June 2006; published 31 August 2006
We study a particle on a ring in the 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 two loop RG for the Caldeira-Legget environment. In the latter case the Aharonov-Bohm (AB) oscillation amplitude is exponential in −R2, 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.