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 ${\bf Ω}$ i.e. bound states of the corresponding Laplace operator $-Δ\_{\bf Ω}$. 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):= -Δ\_{\bf Ω} + {\bf F}. {\bf x} $ has resonances near the discrete eigenvalues of $-Δ\_{\bf Ω}$.