Decoherence of a particle in a ring

We consider a particle coupled to a dissipative environment and derive a perturbative formula for the dephasing rate based on the purity of the reduced probability matrix. We apply this formula to the problem of a particle on a ring, that interacts with a dirty metal environment. At low but finite temperatures we find a dephasing rate ∝ T , and identify dephasing lengths for large and for small rings. These findings shed light on recent Monte Carlo data regarding the effective mass of the particle. At zero temperature we find that spatial fluctuations suppress the possibility of having a power law decay of coherence. Introduction. – The problem of dephasing of a particle coupled to a dissipative environment at temperature T , and in particular in the limit T → 0 has fascinated the mesoscopic community during the last two decades [1–7]. It has been shown [8, 9] that the CaldeiraLeggett (CL) framework [10, 11] can be generalized and that the proper way to characterize the environment is by its form factor S̃(q, ω). Application of the FeynmanVernon formalism [8, 9] and a semiclassical analysis have shown that an interference amplitude Pφ decays with time as Pφ = exp(−pφ(t)) with pφ(t) = t ∫