Sur les semigroupes dynamiques quantiques
Annales mathématiques Blaise Pascal (1996)
- Volume: 3, Issue: 1, page 125-142
- ISSN: 1259-1734
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topRebolledo, Rolando. "Sur les semigroupes dynamiques quantiques." Annales mathématiques Blaise Pascal 3.1 (1996): 125-142. <http://eudml.org/doc/79143>.
@article{Rebolledo1996,
author = {Rebolledo, Rolando},
journal = {Annales mathématiques Blaise Pascal},
keywords = {quantum dynamical semigroups; completely positive weakly continuous; quantum optics; diffusion process; martingale problem; Fokker-Planck equation; entropic diffusion; noncommutative stochastic differential equation; ergodic theorem; stochastic mechanics},
language = {fre},
number = {1},
pages = {125-142},
publisher = {Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal},
title = {Sur les semigroupes dynamiques quantiques},
url = {http://eudml.org/doc/79143},
volume = {3},
year = {1996},
}
TY - JOUR
AU - Rebolledo, Rolando
TI - Sur les semigroupes dynamiques quantiques
JO - Annales mathématiques Blaise Pascal
PY - 1996
PB - Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal
VL - 3
IS - 1
SP - 125
EP - 142
LA - fre
KW - quantum dynamical semigroups; completely positive weakly continuous; quantum optics; diffusion process; martingale problem; Fokker-Planck equation; entropic diffusion; noncommutative stochastic differential equation; ergodic theorem; stochastic mechanics
UR - http://eudml.org/doc/79143
ER -
References
top- 1. E.B. Davies. Quantum dynamical semigroups and the neutron diffusion equation. Rep.Math.Phys., 11:169-188, 1977. Zbl0372.47020MR503331
- 2. F. Fagnola, Characterization of isometric and unitary weakly differentiable cocycles in Fock space, Quantum Probabability and Related Topics, 1993, vol. VIII, 143-164. MR1258327
- 3. F. Fagnola, R. Rebolledo, and C. Saavedra. Quantum flows associated to master equations in quantum optics. J. Math.Phys., 35:1-12, 1994. Zbl0797.60052MR1252096
- 4. F. Fagnola, R. Rebolledo, An ergodic theorem in quantum optics, 1995, à paraître dans les actes du colloque en honneur de A. Frigerio, publiées par l'Université d'Udine. Zbl0842.58040
- 5. F. Fagnola, R. Rebolledo, Sur l'approche de l'équilibre au moyen des flots quantiques, 1995, C.R. Acad.Sci. Paris, sér. I, t.321, 473-476. Zbl0842.58040MR1351100
- 6. A. Frigerio, Stationary states of quantum dynamical semigroups, Comm. in Math. Phys., 1978, vol. 63, 269-276. Zbl0404.46050MR522826
- 7. A. Frigerio et M. Verri, Long-time asymptotic properties of dynamical semigroups on W*—algebras, Math. Zeitschrift, 1982, 180, 275-286. Zbl0471.46048MR661704
- 8. A. Kossakowski V. Gorini and E.C.G. Sudarshan. Completely positive dynamical semigroups of n-level systems. J. Math. Phys., 17:821-825, 1976. MR406206
- 9. G. Lindblad. On the generators of quantum dynamical semigroups. Commun. Math. Phys., 48:119-130, 1976. Zbl0343.47031MR413878
- 10. P.-A. Meyer. Quantum Probability for Probabilists, volume 1538 of Lect. Notes in Math. Springer-Verlag, Berlin, Heidelberg, New York, 1993. Zbl0773.60098MR1222649
- 11. Nelson, E. (1967) Dynamical Theories of Brownian Motion. Princeton University Press. Zbl0165.58502MR214150
- 12. Nelson, E. (1985) Quantum Fluctuations. Princeton University Press. Zbl0563.60001MR783254
- 13. K.R. Parthasarathy and K.B. Sinha. Markov chains as Evans-Hudson diffusions in Fock space. Séminaire de Probabilités, XXIV (1426):362-369, 1988-1989. LNM-Springer. Zbl0699.60065MR1071552
- 14. K.R. Parthasarathy. An Introduction to Quantum Stochastic Calculus, volume 85 of Monographs in Mathematics. Birkhaüser-Verlag, Basel-Boston-Berlin, 1992. Zbl0751.60046MR1164866
- 15. Platen—Rebolledo (1985) Weak Convergence of Semimartingales and Discretization Methods. Stochastic Processes and their Appl.20, 41-58. Zbl0584.60060
- 16. Protter, P. (1990) Stochastic Integration and Differential Equations. A New Approach. Springer-Verlag, 302 p. Zbl0694.60047MR1037262
- 17. Rebolledo (1979) La Méthode des Martingales appliquée à l'étude de la convergence en loi des processus. Bull. Soc. Math. de France, mém. 62, 125 p. Zbl0425.60036MR568153
- 18. Rebolledo (1980) Sur l'existence de solutions à certains probleèmes de semimartingales. C.R. Acad. Sci. Paris, t. 290, 843-846. Zbl0435.60042MR579985
- 19. Rebolledo, R.- Retamal, J.- Saavedra, C. (1992) Diffusion Processes associated to a Laser Model. Journal of Math. Phys. vol. 33, 826-831. MR1145380
- 20. Rebolledo, R. (1992) The Role of weak topologies in Stochastic Mechanics. Ed. Bernoulli, Proceedings IV CLAPEM, Acta Científica Venezolana, Caracas, num., 343-60.
- 21. Stroock, D.W.- Varadhan, S.R.S. (1979) Multidimensional Diffusions Processes. Springer, 338 p. Zbl0426.60069MR532498
- 22. K. Yosida. Functional Analysis. Springer-Yerlag, Berlin, Heidelberg, New York, 3rd. edition, 1971. Zbl0217.16001
- 23. Zheng, W.A. (1985) Tightness results for laws of diffusion processes, application to Stochastic Mechanics, Ann. Inst. Henri Poincaré, vol. 21, n 2, 103-124. Zbl0579.60050MR798890
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