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We study a particle on a ring in presence of various dissipativeenvironments. We develop and solve a variational scheme assuming low frequencydominance. We analyze our solution within a renormalization group (RG) schemeto all orders which reproduces a 2 loop RG for the Caldeira-Legget environment.In the latter case the Aharonov-Bohm (AB) oscillation amplitude is exponentialin -R^2 where R is the ring's radius. For either a charge or an electric dipolecoupled to a dirty metal we find that the metal induces dissipation, howeverthe AB amplitude is ~ R^{-2} for large R, as for free particles. Cold atomswith a large electric dipole may show a crossover between these two behaviors.Comment: 5 pages, added motivations and reference

Interference in the presence of dissipation