Abstract

This paper deals with the asymptotic behavior of a quantum dynamical semigroup (Tt; t ? 0) acting on the algebra of all linear bounded operators on a given Hilbert space. In practice, all these semigroups have a generator which can be written in a well-known form named after Lindblad and Davies. If the semigroup has a faithful normal stationary state ?, necessary and sufficient conditions are derived for the w*-convergence of Tt(X) to T?(X), where T?(X) is the conditional expectation of an element X onto the subalgebra of fixed points. Our main results are expressed in terms of the Lindblad-Davies generator.