Semiclassical wave packet dynamics in Schrodinger equations with periodic potentials

Details Semiclassical wave packet dynamics in Schrodinger equations with periodic potentials Semiclassical wave packet dynamics in Schrodinger equations with periodic potentials

2011-01-17

arxiv.org/abs/1101.3136v2

Discrete and Continuous Dynamical Systems - Series B 17, 3 (2012) 759-774

Physics

Mathematical Physics

15 pages. More explanations. An error fixed in the main result, to include the Berry phase

Scientific paper

10.3934/dcdsb.2012.17.759

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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