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Advances in Mathematical Physics
Volume 2012 (2012), Article ID 309398, 12 pages
http://dx.doi.org/10.1155/2012/309398
Research Article

Resonances for Perturbed Periodic Schrödinger Operator

Institut de Mathématiques de Bordeaux, Université Bordeaux 1, 351, Cours de la Libération, 33405 Talence, France

Received 29 September 2011; Accepted 27 November 2011

Academic Editor: Ali Mostafazadeh

Copyright © 2012 Mouez Dimassi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In the semiclassical regime, we obtain a lower bound for the counting function of resonances corresponding to the perturbed periodic Schrödinger operator 𝑃 ( ) = Δ + 𝑉 ( 𝑥 ) + 𝑊 ( 𝑥 ) . Here 𝑉 is a periodic potential, 𝑊 a decreasing perturbation and a small positive constant.