Quantum dynamics, metastable states, and contractive semigroups

Abstract

The generalized states of a quantum system obtained by analytic continuation of a dense subset of density operators and their time evolutions are studied. The time evolution of metastable states is computed using the generalized states. Certain model theories are taken for explicit study. For factorizable Liouville operators the asymptotic states are shown to give line shapes. Nonfactorizable Liouville operators and their generators are investigated. The generic cases are shown to be contractions of suitable isometries of enveloping systems.