Stark resonances in a quantum waveguide with analytic curvature

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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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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