Unraveling open quantum systems: classical reductions and classical dilations of quantum markov semigroups
Confluentes Mathematici, Tome 1 (2009) no. 1, pp. 123-167.
Publié le :
DOI : 10.1142/S1793744209000055
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Rebolledo, Rolando. Unraveling open quantum systems: classical reductions and classical dilations of quantum markov semigroups. Confluentes Mathematici, Tome 1 (2009) no. 1, pp. 123-167. doi : 10.1142/S1793744209000055. http://archive.numdam.org/articles/10.1142/S1793744209000055/

[1] L. Accardi, A. Frigerio and Y. G. Lu, Quantum Probability and Applications (Springer, 1989) pp. 20.

[2] L. Accardi, A. Frigerio and Y. G. Lu, Comm. Math. Phys. 131, 537 (1990), DOI: 10.1007/BF02098275 .

[3] L. Accardi, Y. G. Lu and I. Volovich, Quantum Theory and Its Stochastic Limit (Springer-Verlag, 2002) p. 493.

[4] R. Alicki and K. Lendi , Quantum Dynamical Semigroups and Applications , Lect. Notes in Physics 286 ( Springer-Verlag , 1987 ) .

[5] G. Alli and G. L. Sewell, J. Math. Phys. 36, 5598 (1995), DOI: 10.1063/1.531279 .

[6] S Attal and A. Joye, J. Statist. Phys. 126, 1241 (2007), DOI: 10.1007/s10955-006-9085-z .

[7] O. Bratteli and D. W. Robinson , Operator Algebras and Quantum Statistical Mechanics, 2 , 2nd edn. ( Springer-Verlag , 1997 ) .

[8] O. Bratteli and D. W. Robinson , Operator Algebras and Quantum Statistical Mechanics, 1 , 2nd edn. ( Springer-Verlag , 1987 ) .

[9] H. J. Carmichael, J. Opt. Soc. Am. B 4, 1588 (1987), DOI: 10.1364/JOSAB.4.001588 .

[10] A. Chebotarev , Lectures on Quantum Probability , Aportaciones Matem. S.M.M 4 ( 2000 ) .

[11] A. Chebotarev and F. Fagnola, J. Funct. Anal. 153, 382 (1998), DOI: 10.1006/jfan.1997.3189 .

[12] E. Christensen and D. E. Evans, J. Lon. Math. Soc. 20, 358 (1979).

[13] E. B. Davies, Rep. Math. Phys. 11, 169 (1977), DOI: 10.1016/0034-4877(77)90059-3 .

[14] C. Dellacherie and P.-A. Meyer , Probabilités et Potentiel I-III ( Hermann , 1975 ) .

[15] L. M. Duan, Phys. Rev. Lett. 85, 3991 (2000), DOI: 10.1103/PhysRevLett.85.3991 .

[16] R. Rebolledo, F. Fagnola and C. Saavedra, J. Math. Phys. 35, 1 (1994).

[17] F. Fagnola, Proyecciones, J. Math. 18, 1 (1999).

[18] F. Fagnola, R. Rebolledo and C. Saavedra, Stochastic Analysis and Mathematical Physics (World Scientific, 1998) pp. 61-71.

[19] F. Fagnola and M. Skeide, Noncommutative Harmonic Analysis with Applications to Probability, Banach Center Publ 78 (Polish Acad. Sci., 2007) pp. 121-132.

[20] C. Gardiner, Phys. Rev. Lett. 56, 1917 (1986), DOI: 10.1103/PhysRevLett.56.1917 .

[21] G. Lindblad, Comm. Math. Phys. 48, 119 (1976), DOI: 10.1007/BF01608499 .

[22] C. M. Mora and R. Rebolledo, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 10, 237 (2007), DOI: 10.1142/S0219025707002725 .

[23] C. M. Mora and R. Rebolledo, Ann. Appl. Probab. 18, 591 (2008), DOI: 10.1214/105051607000000311 .

[24] K. R. Parthasarathy , An Introduction to Quantum Stochastic Calculus , Monographs in Mathematics 85 ( Birkhaüser-Verlag , 1992 ) .

[25] G. Pedersen , Analysis Now , Graduate Texts in Mathematics 118 ( Springer-Verlag , 1989 ) .

[26] R. Rebolledo and D. Spehner, Stochastic Analysis in Mathematical Physics (World Scientific, 2008) pp. 94-108.

[27] R. Rebolledo, Ann. Inst. H. Poincaré Probab. Statist. 41, 349 (2005), DOI: 10.1016/j.anihpb.2004.12.003 .

[28] W. F. Stinespring, Proc. Am. Math. Soc. 6, 211 (1955), DOI: 10.2307/2032342 .

[29] A. Kossakowski, V. Gorini and E. C. G. Sudarshan, J. Math. Phys. 17, 821 (1976).

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