  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.
