Asymptotic completeness in dissipative scattering theory

Abstract

We consider an abstract pseudo-Hamiltonian for the nuclear optical model, given by a dissipative operator of the form $H=H_V-i{C}^{\ast }C$, where $H_V=H_0+V$ is self-adjoint and $C$ is a bounded operator. We study the wave operators associated to $H$ and $H_0$. We prove that they are asymptotically complete if and only if $H$ does not have spectral singularities on the real axis. For Schrödinger operators, the spectral singularities correspond to real resonances.

48 pages