Transience and recurrence of quantum Markov semigroups

Probability Theory and Related Fields

Volumn 126, Issue 2, 2003, Pages 289-306

  Fagnola, Franco ^a   Rebolledo, Rolande ^b  

^a UNIVERSITY OF GENOA   (Italy)

^b PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE   (Chile)

Author keywords

Markov processes; Potential theory; Quantum Markov semigroups

Indexed keywords

EID: 0037972008     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-003-0268-0     Document Type: Article

References (24)

1. Accardi, L., Lu, Y.G., Volovich, I.: Quantum Theory and its Stochastic Limit. Springer-Verlag, 2002
2. Accardi, L., Koroliuk, D.: Quantum Markov chains: The recurrence problem. Quantum Probability and Related Topics VII, 63-73 (1991)
3. Arveson, W.: The heat flow of the CCR algebra. Bull. London Math. Soc. 34 (1), 73-83 (2002)
4. Azéma, J., Duflo, M., Revuz, D.: Propriétés relatives des processus de Markov récurrents. Z. Wahr, und Verw. Gebiete 13, 286-314 (1969)
5. Biane, Ph.: Quelques propriétés du mouvement Brownien non-commutatif. Hommage à P.A. Meyer et J. Neveu. Astérisque 236, 73-102 (1996)
6. Carbone, R.: Exponential ergodicity of a class of quantum Markov semigroups. Tesi di Dottorato. Università di Milano, 2000
7. Chebotarev, A.M., Fagnola, F.: Sufficient conditions for conservativity of minimal quantum dynamical semigroups. J. Funct. Anal. 153, 382-404 (1998)
8. Dellacherie, C., Meyer, P.-A.: Probabilités et potentiel. Chapitres XII-XVI. Second edition, Hermann, Paris, 1987
9. Dixmier, J.: Von Neumann Algebras. North-Holland, 1981
10. Fagnola, F.: Quantum markov semigroups and quantum flows. Proyecciones, Journal of Math. 18(3), 1-144 (1999)
11. Fagnola, F., Rebolledo, R., Saavedra, C.: Quantum flows associated to master equations in quantum optics. J. Math. Phys. 35(1), 1-12 (1994)
12. Fagnola, F., Rebolledo, R.: The approach to equilibrium of a class of quantum dynamical semigroups. Inf. Dim. Anal. Q. Prob, and Rel. Topics 1(4), 1-12 (1998)
13. Fagnola, F., Rebolledo, R.: Subharmonic projections for a Quantum Markov Semigroup. J. Math. Phys. 43, 1074-1082 (2002)
14. Fagnola, F., Rebolledo, R.: Lectures on the Qualitative Analysis of Quantum Markov Semigroups. Quantum Probability and White Noise Analysis. World Scientific XIV, 197-240 (2002)
15. Frigerio, A., Verri, M.: Long-time asymptotic properties of dynamical semigroups on w*-algebras. Math. Zeitschrift 180, 275-286 (1982)
16. Getoor, R.K.: Transience and recurrence of Markov processes. Séminaire de Probabilités, XIV (Paris, 1978/1979), pp. 397-409, Lecture Notes in Math., 784, Springer, Berlin, 1980
17. Gisin, N., Percival, I.: The quantum-state diffusion model applied to open systems. J. Phys. A 25, 5677 (1992)
18. Kato, T.: Perturbation theory for linear operators. Corr. printing of the 2nd ed. Springer-Verlag, N.Y., 1980
19. Meyer, P.-A.: Quantum Probability for Probabilists, volume 1538 of Lect. Notes in Math. Springer-Verlag, Berlin, Heidelberg, New York, 1993
20. Parthasarathy, K.R.: An Introduction to Quantum Stochastic Calculus, volume 85 of Monographs in Mathematics. Birkhaüser-Verlag, Basel-Boston-Berlin, 1992
21. Percival, I.: Quantum state diffusion, Cambridge Univ. Press, Cambridge, 1998
22. Perry, P.A.: Scattering Theory by the Enss Method. Harwood Academic Publishers
23. Rebolledo, R.: On the recurrence of Quantum Dynamical Semigroups. Proc. ANES-TOC'96. World Scientific Pub., 130-141 (1997)
24. Sinha, K.: On the absolutely and singularly continuous subspaces in Scattering Theory. Ann. I.H.P. ser. A 26, 263-277