{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T17:40:46Z","timestamp":1770918046426,"version":"3.50.1"},"reference-count":21,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2007,12]]},"abstract":"<jats:p> 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 H<jats:sub>S<\/jats:sub>, acting on h, interacting with a Gaussian, gauge invariant, reservoir. The selfadjoint operator H<jats:sub>S<\/jats:sub> determines a privileged orthonormal basis of h. These semigroups leave invariant diagonal and off-diagonal bounded operators with respect to this basis. The action on diagonal operators describes a classical Markov jump process. We construct generic semigroups from their formal generators by the minimal semigroup method and discuss their conservativity (uniqueness). When the semigroup is irreducible we prove uniqueness of the equilibrium state and show that, starting from an arbitrary initial state, the semigroup converges towards this state. We also prove that the exponential speed of convergence of the quantum Markov semigroup coincides with the exponential speed of convergence of the classical (diagonal) semigroup towards its unique invariant measure. The exponential speed is computed or estimated in some examples. <\/jats:p>","DOI":"10.1007\/s11080-007-9066-y","type":"journal-article","created":{"date-parts":[[2007,12,10]],"date-time":"2007-12-10T15:24:59Z","timestamp":1197300299000},"page":"425-444","source":"Crossref","is-referenced-by-count":29,"title":["Generic Quantum Markov Semigroups: the Gaussian Gauge Invariant Case"],"prefix":"10.1142","volume":"14","author":[{"given":"Raffaella","family":"Carbone","sequence":"first","affiliation":[{"name":"Dipartimento di Matematica, Universit\u00e0 di Pavia, Via Ferrata 1, I-27100 Pavia, Italy"}]},{"given":"Franco","family":"Fagnola","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy"}]},{"given":"Skander","family":"Hachicha","sequence":"additional","affiliation":[{"name":"Institut Pr\u00e9paratoire aux \u00c9tudes d'Ing\u00e9nieurs 2, Rue Jawaharlal Nehru Monfleury 1008, Tunis, Tunisia"}]}],"member":"219","published-online":{"date-parts":[[2012,4,17]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/S0219025706002548"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/s11080-005-4488-x"},{"key":"rf3","unstructured":"L.\u00a0Accardi and S.\u00a0Kozyrev, QP\u2013PQ: Quantum Probab. White Noise Anal., Lectures on Quantum Interacting Particle Systems, in: Quantum interacting particle systems (Trento, 2000)\u00a014, eds. L.\u00a0Accardi and F.\u00a0Fagnola (World Sci. 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