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arXiv · 1101.3136

Semiclassical wave packet dynamics in Schrodinger equations with periodic potentials

Rémi Carles·Christof Sparber
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Abstract

We consider semiclassically scaled Schrodinger 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 obtained by Peierl's substitution, and involve a slowly varying envelope whose dynamics is governed by a homogenized Schrodinger equation with time-dependent effective mass. The corresponding adiabatic decoupling of the slow and fast degrees of freedom is shown to be valid up to Ehrenfest time scales.

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Rémi Carles, Christof Sparber. 2011-01-17. Semiclassical wave packet dynamics in Schrodinger equations with periodic potentials. https://doi.org/10.3934/dcdsb.2012.17.759

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