Seminarium KMMF "Teoria Dwoistości"

In this talk, we will consider an abstract pseudo-hamiltonian given by a dissipative operator of the form H=H_V-iC^*C, where H_V=H_0+V is self-adjoint and C is a bounded operator. Such operators are frequently used to study scattering theory for dissipative quantum systems. We will recall conditions impliying the existence of the wave operators associated to H and H_0, and we will see that they are assymptotically complete if and only if H has no spectral singularities in its essential spectrum. In mathematical physics, spectral singularities have been considered in many different contexts. We will review several possibilities equivalent definitions of a spectral singularity. For dissipative Schrodinger operators, a spectral singularity corresponds to a real resonance, or, equivalently, to a point of the positive real axis where the scattering matrix is not invertible. The talk is based on two articles. The first ons is joint work with Jurg Frohlich and the second one is joint work with Francois Nicoleau.