Dephasing of a particle in a dissipative environment

The motion of a particle in a ring of length L is influenced by a dirty metal environment whose fluctuations are characterized by a short correlation distance $\ell << L$. We analyze the induced decoherence process, and compare the results with those obtained in the opposing Caldeira-Leggett limit ($\ell >> L$). A proper definition of the dephasing factor that does not depend on a vague semiclassical picture is employed. Some recent Monte-Carlo results about the effect of finite temperatures on "mass renormalization" in this system are illuminated.