Generic nature of asymptotic completeness in dissipative scattering theory

Abstract

We review recent results obtained in the scattering theory of dissipative quantum systems representing the long-time evolution of a system [Formula: see text] interacting with another system [Formula: see text] and susceptible of being absorbed by [Formula: see text]. The effective dynamics of [Formula: see text] is generated by an operator of the form [Formula: see text] on the Hilbert space of the pure states of [Formula: see text], where [Formula: see text] is the self-adjoint generator of the free dynamics of [Formula: see text], [Formula: see text] is symmetric and [Formula: see text] is bounded. The main example is a neutron interacting with a nucleus in the nuclear optical model. We recall the basic objects of the scattering theory for the pair [Formula: see text], as well as the results, proven in [10, 11], on the spectral singularities of [Formula: see text] and the asymptotic completeness of the wave operators. Next, for the nuclear optical model, we show that asymptotic completeness generically holds.