SEMINAIRE MERCREDI 22 OCTOBRE 2008
14h
Salle Séminaire 5
Centre de Physique Théorique
Marseille-Luminy

Hagen Neidhardt
WIAS Berlin

Title: Scattering theory for open quantum system

Abstract: Pseudo-Hamiltonians or maximal dissipative operators are often used to describe
open quantum systems. Their minimal self-adjoint dilations which are
called in this concept quasi-Hamiltonians, are regarded as the Hamiltonians of a
closed quantum systems containing the open ones. However, the nice interpretations
suffers from the observation that the quasi-Hamiltonian is necessarily not
semi-bounded from below. However, choosing for each energy another quasi-
Hamiltonian in a suitable manner one gets a quasi-Hamiltonian which can be
semi-bounded from below. Surprisingly it turns out that the scattering matrix
of a naturally posed scattering problem can be recovered using the scattering
matrix of an appropriate posed Lax-Phillips scattering problem for a single
pseudo-Hamiltonian. The theory of boundary triplets, Weyl functions, etc. is
essentially used.