By numerical simulations and analytical studies, we show that the phenomenon of microwave-induced resistance oscillations can be understood as a classical memory effect caused by re-collisions of electrons with scattering centers after a cyclotron period. We develop a Drude-like approach to magneto-transport in presence of a microwave field, taking account of memory effects, and find an excellent agreement between numerical and analytical results, as well as a qualitative agreement with experiment.
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