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 $-\Delta\_{ { \bf \Omega}}$.
Categories: math.SP math-ph math.MP