Scattering theory for lattice operators in dimension $d\geq 3$
Talk by Prof. Dr. Hermann Schulz-Baldes
Date: 11.03.11 Time: 10.45 - 11.45 Room: ETH HIT F 31.2
Abstract: This talk analyzes the scattering theory for periodic tight-binding Hamiltonians perturbed by a finite range impurity. The classical energy gradient flow is used to construct a conjugate (or dilation) operator to the unperturbed Hamiltonian. For dimension $d\geq 3$ the wave operator is given by an explicit formula in terms of this dilation operator. From this also the scattering and time delay operators can be read off. Using the index theorem approach a Levinson theorem for these operators also in presence of embedded eigenvalues and threshold singularities can be deduced. This is based on joint work with J. Bellissard.