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 $\mathbf{\Omega }$ i.e. bound states of the corresponding Laplace operator $-\Delta \_\mathbf{\Omega }$. Here the curvature of the guide is supposed to satisfy some assumptions of analyticity, and decays as $O(|s{|}^{-\epsilon }),\epsilon >3$ at infinity. We show that under conditions on the electric field $\mathbf{F}$, $\mathbf{H}(F):=-\Delta \_\mathbf{\Omega }+\mathbf{F}.\mathbf{x}$ has resonances near the discrete eigenvalues of $-\Delta \_\mathbf{\Omega }$.

Cited by in corpus (1)

• Fermi's golden rule in tunneling models with quantum waveguides perturbed by Kato class measures