Localization for the Schr\"{o}dinger equation in a locally periodic medium
Analysis of PDEs
2015-02-10 v1
Abstract
We study the homogenization of a Schr\"{o}dinger equation in a locally periodic medium. For the time and space scaling of semi-classical analysis we consider well-prepared initial data that are concentrated near a stationary point (with respect to both space and phase) of the energy, i.e. the Bloch cell eigenvalue. We show that there exists a localized solution which is asymptotically given as the product of a Bloch wave and of the solution of an homogenized Schr\"{o}dinger equation with quadratic potential.
Keywords
Cite
@article{arxiv.1502.02455,
title = {Localization for the Schr\"{o}dinger equation in a locally periodic medium},
author = {Grégoire Allaire and Mariapia Palombaro},
journal= {arXiv preprint arXiv:1502.02455},
year = {2015}
}