Effect of dissipative environments on Aharonov-Bohm oscillations of a particle

A charged particle of mass M on a ring of radius R is coupled to various environments. With Monte-Carlo methods we evaluate the curvature of the Aharonov-Bohm oscillations. For Caldeira-Legget bath of oscillators we find the origin of big descepancies between results of different groups. For a charged particle in a dirty metal environment we find a quantum phase transition at a critical Rc. At low temperatures T the curvature has the form 1/M*R ² with an R independent M > M in the R > R_c phase, while M* rapidly approached M in the R < R_c phase. The approach to T = 0 defines diverging length scales ∼T-ⁿ with η ≈ 1 and η ≈ 1/4 in the large and small R phases, respectively. Our preliminary results for a particle with electric dipole in a dirty metal environment for large R and low temperatures show an R independent saturation of M* > M as in a charged particle case.