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Abstract: We introduce a switching mechanism in quantum systems induced by the combined effects of a periodic driving and a weak coupling to a heat bath. For an asymmetric double well potential the stationary probability distribution can be switched between the lower and the upper well by a very weak driving amplitude. We explain this switching mechanism by an effective rate equation, which combines the effects of the coherent driving at an avoided crossing of two Floquet states with the incoherent bath coupling resulting in the population of an unrelated state in the upper well.