Exponential $L_2$-convergence of quantum Markov semigroups on~$\mathscr B(h)$
Matematičeskie zametki, Tome 68 (2000) no. 4, pp. 523-538.

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R. Carbone; F. Fagnola. Exponential $L_2$-convergence of quantum Markov semigroups on~$\mathscr B(h)$. Matematičeskie zametki, Tome 68 (2000) no. 4, pp. 523-538. http://geodesic.mathdoc.fr/item/MZM_2000_68_4_a3/

[1] Fagnola F., “Quantum Markov Semigroups and Quantum Markov Flows”, Proyecciones (to appear)

[2] Chen M. F., “Estimation of spectral gap for Markov chains”, Acta Math. Sinica (N.S.), 12:4 (1996), 337–360 | MR | Zbl

[3] Liggett T., “Exponential $L_2$ convergence of attractive reversible nearest particle systems”, Ann. Probab., 17 (1989), 403–432 | DOI | MR | Zbl

[4] Saloff-Coste L., “Lectures on finite Markov chains”, Lectures on Probability Theory and Statistics (St. Flour, 1996), Lecture Notes in Math., 1665, Springer, New York, 1997, 301–413 | MR | Zbl

[5] Ohya M., Petz D., Quantum Entropy and Its Use, Springer, New York, 1995

[6] Jorgensen P. E. T., “Approximately reducing subspaces for unbounded operators”, J. Funct. Anal., 23 (1976), 392–414 | DOI | MR

[7] Goldstein S., Lindsay J. M., “KMS-symmetric semigroups”, Math. Z., 219 (1995), 591–608 | DOI | MR | Zbl

[8] Majewsky W. A., Streater R. F., “Detailed balance and quantum dynamical maps”, J. Phys. A, 31 (1998), 7981–7995 | DOI | MR

[9] Chebotarev A. M., “The theory of dynamical semigroups and its applications”, Probability Theory and Mathematical Statistics, V. I (Vilnius, 1989), Mokslas, Vilnius, 1990, 217–227 | MR

[10] Karlin S., Taylor H. M., A First Course on Stochastic Processes, Acad. Press, New York, 1975 | Zbl

[11] Pazy A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1975

[12] Carbone R., “Exponential $L^2$-convergence of some quantum Markov semigroups related to birth-death processes”, Stochastic Analysis and Mathematical Physics ANESTOC'98 (Santiago, 1998) (to appear) | Zbl

[13] Reed M., Simon B., Methods of Modern Mathematical Physics. Vol. II. Fourier Analysis. Self-Adjointness, Acad. Press, New York, 1975 | Zbl

[14] Cipriani F., Fagnola F., Lindsay J. M., “Feller property and Poincaré inequality for the quantum Ornstein–Uhlenbeck semigroups”, Comm. Math. Phys. (to appear)

[15] Fagnola F., Rebolledo R., Saavedra C., “Quantum flows associated to master equations in quantum optics”, J. Math. Phys., 35 (1994), 1–12 | DOI | MR | Zbl