Received 18 June 2010; revised 8 September 2010; published 19 October 2010
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/τ2 decay in imaginary time.