The Approach to Equilibrium of a Class of Quantum Dynamical Semigroups

This paper deals with the asymptotic behavior of a quantum dynamical semigroup Formula: see text 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 ρ, necessary and sufficient conditions are derived for the w * -convergence of Formula: see text to Formula: see text, where Formula: see text 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 .