Landau-Zener transitions in a dissipative environment: numerically exact results.

We study Landau-Zener transitions in a dissipative environment by means of the numerically exact quasiadiabatic propagator path integral. It allows to cover the full range of the involved parameters. We discover a nonmonotonic dependence of the transition probability on the sweep velocity which is explained in terms of a simple phenomenological model. This feature, not captured by perturbative approaches, results from a nontrivial competition between relaxation and the external sweep.