caa a22 4500 475740998 CHVBK 20180406123459.0 cr unu---uuuuu 170329e20001001xx s 000 0 eng 10.1007/BF02676724 doi (NATIONALLICENCE)springer-10.1007/BF02676724 Exponential L 2-convergence of quantum Markov semigroups on $$\mathcal{B}(h)$$ [Elektronische Daten] [R. Carbone, F. Fagnola] With a quantum Markov semigroup (Τ t ) t≥0 on $$\mathcal{B}(h)$$ , whichhas a faithful normal invariant state ρ, we associate semigroupsT (s) (s∈[0],[1]) on the set of Hilbert-Schmidt operators onh defined by the rule $$T_t^{(s)} (\rho ^{s/{\text{2}}} x\rho ^{(1 - s)/{\text{2}}} ) = \rho ^{s/{\text{2}}} \mathcal{T}_t (x)\rho ^{(1 - s)/{\text{2}}} $$ . This allows us to use spectral theory to study the infinitesimal generatorL (s) of the semigroupT (s) and deduce information on the rate of the decay to equilibrium of Τ by means of estimates of the spectral gap ofL (s) . Fors=1/2, this method is applied to a class of quantum Markov semigroups on $$\mathcal{B}(h)$$ . We prove simple but reasonably general sufficient conditions, as well as necessary and sufficient conditions, for the gap(L (1/2)) to be positive. The exact value of the gap(L (1/2)) is computed or estimated for a certain class of equations motivated by classical probability or physical applications. Kluwer Academic/Plenum Publishers, 2000 Markov semigroup nationallicence quantum Markov semigroup nationallicence invariant state nationallicence decay to equilibrium nationallicence spectral gap nationallicence symmetric imbedding of operators nationallicence exponential rate nationallicence quantum birth-and-death process nationallicence Carbone R. Departmento di Matematica, Università di Milano, Milano, Italia aut Fagnola F. Dipartmento di Matematica, Università di Genova, Genova, Italia aut Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/4(2000-10-01), 452-463 0001-4346 68:4<452 2000 68 11006 https://doi.org/10.1007/BF02676724 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02676724 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Carbone R. Departmento di Matematica, Università di Milano, Milano, Italia aut NATIONALLICENCE 700 1- Fagnola F. Dipartmento di Matematica, Università di Genova, Genova, Italia aut NATIONALLICENCE 773 0- Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/4(2000-10-01), 452-463 0001-4346 68:4<452 2000 68 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer