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We study Landau-Zener transitions in a dissipative environment by means ofthe numerically exact quasiadiabatic propagator path-integral. It allows tocover the full range of the involved parameters. We discover a nonmonotonicdependence of the transition probability on the sweep velocity which isexplained in terms of a simple phenomenological model. This feature, notcaptured by perturbative approaches, results from a nontrivial competitionbetween relaxation and the external sweep.

Landau Zener transitions in a dissipative environment: Numerically exact results