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In this paper we study the influence of an electric field on a two dimen-sional waveguide. We show that bound states that occur under a geometrical deformation of the guide turn into resonances when we apply an electric field of small intensity having a nonzero component on the longitudinal direction of the system. MSC-2010 number: 35B34,35P25, 81Q10, 82D77.
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 su
We define resonances for finitely perturbed quantum walks as poles of the scattering matrix in the lower half plane. We show a resonance expansion which describes the time evolution in terms of resonances and corresponding Jordan chains. In particula
We make a spectral analysis of the massive Dirac operator in a tubular neighborhood of an unbounded planar curve,subject to infinite mass boundary conditions. Under general assumptions on the curvature, we locate the essential spectrum and derive an
The question of whether it is possible to compute scattering resonances of Schrodinger operators - independently of the particular potential - is addressed. A positive answer is given, and it is shown that the only information required to be known a
We consider the Dirichlet Laplacian $H_gamma$ on a 3D twisted waveguide with random Anderson-type twisting $gamma$. We introduce the integrated density of states $N_gamma$ for the operator $H_gamma$, and investigate the Lifshits tails of $N_gamma$, i