Landau-Zener transitions and dissipation in a mesoscopic ring

We investigate the interplay between Landau-Zener transitions and dissipation in a mesoscopic ring, which encloses a Linearly time-dependent magnetic flux driving the ring's electrons by a constant induced electric field. Whereas the kinetic energy and the current carried by the electrons show dynamical localization in the nondissipative case, this quantum-interference effect is destroyed and replaced by the relaxation into a periodic limit cycle, if the coupling to a heat bath of phonons is switched on. The dissipative time scales of decoherence and relaxation are studied in detail with an extended master equation formalism for the electrons' density operator, which includes quantum statistics effects. It is possible to absorb the periodic influence of the external driving within the representation of generalized quasienergy states, which we introduce in the discussion of the relaxation time.