# Stark resonances in a quantum waveguide with analytic curvature

1 CPT - E8 Dynamique quantique et analyse spectrale
CPT - Centre de Physique Théorique - UMR 7332
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 $-\Delta_{ {\bf \Omega} }$.
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Cited literature [12 references]

https://hal.archives-ouvertes.fr/hal-01292418
Contributor : Philippe Briet <>
Submitted on : Friday, June 24, 2016 - 4:31:38 PM
Last modification on : Thursday, March 15, 2018 - 4:56:08 PM
Long-term archiving on : Sunday, September 25, 2016 - 12:05:20 PM

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Philippe Briet, Mounira Gharsalli. Stark resonances in a quantum waveguide with analytic curvature. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2016, 49 (49), pp.495202. ⟨10.1088/1751-8113/49/49/495202⟩. ⟨hal-01292418v3⟩

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