# Stark resonances in a quantum waveguide with analytic curvature

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1 CPT - E9 Dynamique quantique et analyse spectrale CPT - Centre de Physique Théorique - UMR 7332 2 CPT - Centre de Physique Théorique - UMR 7332 3 Université de Tunis - El Manar II

Abstract : We investigate the influence of an electric field on trapped modes arising in a two-dimensional curved quantum waveguide ${\bf \Omega}$ i.e. bound states of the corresponding Laplace operator $-\Delta { {\bf \Omega} }$. Here the curvature of the guide is supposed to satisfy some assumptions of analyticity, and decays as $O|s|^{-\varepsilon}, \varepsilon >3$ at infinity. We show that under conditions on the electric field $\bf F$, ${\bf H}F:= -\Delta { {\bf \Omega} } + {\bf F}. {\bf x}$ has resonances near the discrete eigenvalues of $-\Delta { {\bf \Omega} }$.

Keywords : Waveguide MSC-2010 number: 35B34 Operator Theory Schrödinger Operators Resonance 35P25 81Q10 82D77

Autor: Philippe Briet - Mounira Gharsalli -

Fuente: https://hal.archives-ouvertes.fr/

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