Scattering matrices for dissipative quantum systems.

We consider a quantum system S interacting with another system S ′ and susceptible of being absorbed by S ′. The effective, dissipative dynamics of S is supposed to be generated by an abstract pseudo-Hamiltonian of the form H = H 0 + V − i C ⁎ C. The generator of the free dynamics, H 0 , is self-adjoint, V is symmetric and C is bounded. We study the scattering theory for the pair of operators (H , H 0). We establish a representation formula for the scattering matrices and identify a necessary and sufficient condition to their invertibility. This condition rests on a suitable notion of spectral singularity. Our main application is the nuclear optical model, where H is a dissipative Schrödinger operator and spectral singularities correspond to real resonances. [ABSTRACT FROM AUTHOR]