Stark resonances in a quantum waveguide with analytic curvature


الملخص بالإنكليزية

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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