Semiclassical wave packet dynamics in Schrodinger equations with periodic potentials
Mathematical Physics
2012-01-16 v2 Analysis of PDEs
math.MP
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.
Cite
@article{arxiv.1101.3136,
title = {Semiclassical wave packet dynamics in Schrodinger equations with periodic potentials},
author = {Rémi Carles and Christof Sparber},
journal= {arXiv preprint arXiv:1101.3136},
year = {2012}
}
Comments
15 pages. More explanations. An error fixed in the main result, to include the Berry phase