Quantum Markov Semigroups: Structure and Asymptotics
نویسنده
چکیده
We study the structure of a quantum Markov semigroup (Tt)t≥0 on a von Neumann algebra A starting from its decomposition by means of the transient and recurrent projections. The existence of invariant states and convergence to invariant state is also discussed. Applications to quantum Markov semigroups with Lindblad type infinitesimal generator are analysed.
منابع مشابه
Stability of additive functional equation on discrete quantum semigroups
We construct a noncommutative analog of additive functional equations on discrete quantum semigroups and show that this noncommutative functional equation has Hyers-Ulam stability on amenable discrete quantum semigroups. The discrete quantum semigroups that we consider in this paper are in the sense of van Daele, and the amenability is in the sense of Bèdos-Murphy-Tuset. Our main result genera...
متن کاملGenerators of KMS Symmetric Markov Semigroups on B(h) Symmetry and Quantum Detailed Balance
We find the structure of generators of norm continuous quantum Markov semigroups on B(h) that are symmetric with respect to the scalar product tr(ρxρy) induced by a faithful normal invariant state invariant state ρ and satisfy two quantum generalisations of the classical detailed balance condition related with this non-commutative notion of symmetry: the socalled standard detailed balance condi...
متن کاملDecomposition and Classification of Generic Quantum Markov Semigroups: The Gaussian Gauge Invariant Case
Abstract We study a class of generic quantum Markov semigroups on the algebra of all bounded operators on a Hilbert space h arising from the stochastic limit of a discrete system with generic Hamiltonian HS , acting on h, interacting with a Gaussian, gauge invariant, reservoir. The self-adjoint operator HS determines a privileged orthonormal basis of h. These semigroups leave invariant diagonal...
متن کاملA Cycle Decomposition and Entropy Production for Circulant Quantum Markov Semigroups
We propose a definition of cycle representation for Quantum Markov Semigroups (qms) and Quantum Entropy Production Rate (QEPR) in terms of the ρ-adjoint. We introduce the class of circulant qms, which admit non-equilibrium steady states but exhibit symmetries that allow us to compute explicitly the QEPR, gain a deeper insight into the notion of cycle decomposition and prove that quantum detaile...
متن کاملSpatial Markov Semigroups Admit Hudson-Parthasarathy Dilations
For many Markov semigroups dilations in the sense of Hudson and Parthasarathy, that is a dilation which is a cocycle perturbation of a noise, have been constructed with the help of quantum stochastic calculi. In these notes we show that every Markov semigroup on the algebra of all bounded operators on a separable Hilbert space that is spatial in the sense of Arveson, admits a Hudson-Parthasarat...
متن کامل