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Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series B Année : 2012

Semiclassical wave packet dynamics in Schrodinger equations with periodic potentials

Résumé

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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Dates et versions

hal-00556468 , version 1 (16-01-2011)
hal-00556468 , version 2 (13-03-2011)

Identifiants

Citer

Rémi Carles, Christof Sparber. Semiclassical wave packet dynamics in Schrodinger equations with periodic potentials. Discrete and Continuous Dynamical Systems - Series B, 2012, 17 (3), pp.759-774. ⟨10.3934/dcdsb.2012.17.759⟩. ⟨hal-00556468v2⟩
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