posted on 2012-08-15, 00:00authored byR´emi Carles, Christof Sparber
We consider semiclassically scaled Schr¨odinger equations with an
external potential and a highly oscillatory periodic potential. We construct asymptotic
solutions in the form of semiclassical wave packets. These solutions are concentrated (both, in space and in frequency) around the effective semiclassical phase-space flow, and involve a slowly varying envelope whose dynamics is governed by a homogenized Schr¨odinger equation with time-dependent
effective mass tensor. The corresponding adiabatic decoupling of the slow and
fast degrees of freedom is shown to be valid up to Ehrenfest time scales.