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Semiclassical Wave Packet Dynamics In Schrodinger Equations With Periodic Potentials

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Title: Semiclassical Wave Packet Dynamics In Schrodinger Equations With Periodic Potentials
Author(s): Carles, R´emi; Sparber, Christof
Abstract: 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.
Issue Date: 2012-05
Publisher: American Institute of Mathematical Sciences
Citation Info: Carles, R. & Sparber, C. 2012. Semiclassical Wave Packet Dynamics in Schrodinger Equations with Periodic Potentials. Discrete and Continuous Dynamical Systems-Series B, 17(3): 759-774. DOI: 10.3934/dcdsb.2012.17.759
Type: Article
Description: © 2012 by American Institute of Mathematical Sciences, Discrete and Continuous Dynamical Systems - Series B DOI: 10.3934/dcdsb.2012.17.759
ISSN: 1531-3492
Date Available in INDIGO: 2012-08-15

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