Decoherence of quantum Markov semigroups

Rebolledo, Rolando

doi:10.1016/j.anihpb.2004.12.003

Rebolledo, Rolando

Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 3, pp. 349-373.

MR Zbl | 2 citations dans Numdam

DOI : 10.1016/j.anihpb.2004.12.003

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     title = {Decoherence of quantum {Markov} semigroups},
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Rebolledo, Rolando. Decoherence of quantum Markov semigroups. Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 3, pp. 349-373. doi : 10.1016/j.anihpb.2004.12.003. http://www.numdam.org/articles/10.1016/j.anihpb.2004.12.003/

Bibliographie
Cité par

[1] L. Accardi, Y.G. Lu, I. Volovich, Quantum Theory and its Stochastic Limit, Springer-Verlag, 2002. | MR | Zbl

[2] R. Alicki, K. Lendi, Quantum Dynamical Semigroups and Applications, Lecture Notes in Phys., vol. 286, Springer-Verlag, 1987. | MR | Zbl

[3] Ph. Biane, Quelques propriétés du mouvement Brownien non-commutatif. Hommage à P.A. Meyer et J. Neveu, Astérisque 236 (1996) 73-102. | Numdam | MR | Zbl

[4] Ph. Blanchard, R. Olkiewicz, Decoherence induced transition from quantum to classical dynamics, Rev. Math. Phys. 15 (2003) 217-243. | MR | Zbl

[5] O. Bratteli, D.W. Robinson, Operator Algebras and Quantum Statistical Mechanics, vol. 1, Springer-Verlag, 1987. | MR | Zbl

[6] O. Bratteli, D.W. Robinson, Operator Algebras and Quantum Statistical Mechanics, vol. 2, Springer-Verlag, 1996. | Zbl

[7] M. Brune et al., Phys. Rev. Lett. 77 (1996) 4887.

[8] A.M. Chebotarev, F. Fagnola, Sufficient conditions for conservativity of minimal quantum dynamical semigroups, J. Funct. Anal. 153 (1998) 382-404. | MR | Zbl

[9] A.M. Chebotarev, Lectures on Quantum Probability, Aportaciones Matemáticas, Ser. Textos, vol. 14, Soc. Mat. Mexicana, México, 2000. | MR | Zbl

[10] E. Christensen, D.E. Evans, Cohomology of operator algebras and quantum dynamical semigroups, J. London Math. Soc. 20 (1979) 358-368. | MR | Zbl

[11] E.B. Davies, Quantum dynamical semigroups and the neutron diffusion equation, Rep. Math. Phys. 11 (1977) 169-188. | MR | Zbl

[12] C. Dellacherie, P.-A. Meyer, Probabilités et potentiel. Chapitres XII-XVI, Hermann, Paris, 1987. | MR | Zbl

[13] G. Dell Antonio, On Decoherence, J. Math. Phys. 44 (2003) 4939-4956. | MR | Zbl

[14] F. Fagnola, Quantum Markov semigroups and quantum flows, Proyecciones J. Math. 18 (3) (1999) 1-144. | MR | Zbl

[15] F. Fagnola, R. Rebolledo, The approach to equilibrium of a class of quantum dynamical semigroups, Infinite Dimensional Anal. Quantum Probab. Related Topics 1 (4) (1998) 1-12. | MR | Zbl

[16] F. Fagnola, R. Rebolledo, On the existence of invariant states for quantum dynamical semigroups, J. Math. Phys. 42 (2001) 1296-1308. | MR | Zbl

[17] F. Fagnola, R. Rebolledo, Subharmonic projections for a quantum Markov semigroup, J. Math. Phys. 43 (2002) 1074-1082. | MR | Zbl

[18] F. Fagnola, R. Rebolledo, Transience and recurrence of quantum Markov semigroups, Probab. Theory Related Fields 126 (2003) 289-306. | MR | Zbl

[19] A. Frigerio, M. Verri, Long-time asymptotic properties of dynamical semigroups on $w^{*}$ -algebras, Math. Z. (1982). | Zbl

[20] D. Giulini et al., Decoherence and the Appearance of a Classical world in Quantum Theory, Springer, Heidelberg, 1996. | Zbl

[21] V. Gorini, A. Kossakowski, E.C.G. Sudarshan, Completely positive dynamical semigroups of n-level systems, J. Math. Phys. 17 (1976) 821-825. | MR

[22] A. Holevo, Statistical Structure of Quantum Theory, Lecture Notes in Phys., vol. 67, Springer-Verlag, 2001. | MR | Zbl

[23] T.M. Liggett, Interacting Particle Systems, Springer-Verlag, New York, 1985. | MR | Zbl

[24] T.M. Liggett, Stochastic Interacting Systems: Contact, Voter and Exclusion Processes, Springer-Verlag, Berlin, 1999. | MR | Zbl

[25] G. Lindblad, On the generators of quantum dynamical semigroups, Commun. Math. Phys. 48 (1976) 119-130. | MR | Zbl

[26] A. Majewski, R.F. Streater, Detailed balance and quantum dynamical maps, J. Phys. A 31 (1998) 7981-7995. | MR | Zbl

[27] P.-A. Meyer, Quantum Probability for Probabilists, Lecture Notes in Math., vol. 1538, Springer-Verlag, Berlin, 1993. | MR | Zbl

[28] C.J. Myatt et al., Nature 403 (2000) 269.

[29] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, 1983. | MR | Zbl

[30] K.R. Parthasarathy, An Introduction to Quantum Stochastic Calculus, Monographs in Math., vol. 85, Birkhaüser, Basel, 1992. | MR | Zbl

[31] W.F. Stinespring, Positive functions on $C^{*}$ -algebras, Proc. Amer. Math. Soc. 6 (1955) 211-216. | Zbl

[32] G.K. Pedersen, Analysis Now, Graduate Texts in Math., vol. 118, Springer-Verlag, 1989. | MR | Zbl

[33] W.T. Strunz, Decoherence in quantum physics, in: Buchleitner A., Hornberger K. (Eds.), Coherent Evolution in Noisy Environments, Lecture Notes in Phys., vol. 611, Springer-Verlag, 2002, pp. 199-233. | MR

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