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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 particular, the decay rate of the survival probability is given by the imaginary part of resonances and the multiplicity. We prove generic simplicity of the resonances, although there are quantum walks with multiple resonances.
We consider the Dirichlet Laplacian in a three-dimensional waveguide that is a small deformation of a periodically twisted tube. The deformation is given by a bending and an additional twisting of the tube, both parametrized by a coupling constant $d
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 havin
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
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 twisted waveguide $Omega_theta$, i.e. the domain obtained by the rotation of the bounded cross section $omega subset {mathbb R}^{2}$ of the straight tube $Omega : = omega times {mathbb R}$ at angle $theta$ which depends on the variabl