The Aharonov-Bohm effect in presence of dissipative environments

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.