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Resonances for Slowly Varying Perturbations of a Periodic Schrödinger Operator

Published online by Cambridge University Press:  20 November 2018

Mouez Dimassi
Mouez Dimassi*
Affiliation:
Université de Paris-Nord, Département de Mathématiques, UMR 7539, Institut Galilée, 93430 Villetaneuse, France
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Abstract

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We study the resonances of the operator $P(h)\,=\,-{{\Delta }_{x}}\,+\,V(x)\,+\,\varphi (hx)$. Here $V$ is a periodic potential, $\varphi $ a decreasing perturbation and $h$ a small positive constant. We prove the existence of shape resonances near the edges of the spectral bands of ${{P}_{0\,}}=\,-{{\Delta }_{x}}\,+\,V(x)$, and we give its asymptotic expansions in powers of ${{h}^{\frac{1}{2}}}$.

Keywords

35P9947A6047A40
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 54 , Issue 5 , 01 October 2002 , pp. 998 - 1037
Copyright
Copyright © Canadian Mathematical Society 2002

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