Decoherence of quantum Markov semigroups

Rolando Rebolledo

Annales de l'I.H.P. Probabilités et statistiques (2005)

  • Volume: 41, Issue: 3, page 349-373
  • ISSN: 0246-0203

How to cite

top

Rebolledo, Rolando. "Decoherence of quantum Markov semigroups." Annales de l'I.H.P. Probabilités et statistiques 41.3 (2005): 349-373. <http://eudml.org/doc/77849>.

@article{Rebolledo2005,
author = {Rebolledo, Rolando},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {quantum Markov semigroup; decoherence; limit behaviour; invariant subalgebras},
language = {eng},
number = {3},
pages = {349-373},
publisher = {Elsevier},
title = {Decoherence of quantum Markov semigroups},
url = {http://eudml.org/doc/77849},
volume = {41},
year = {2005},
}

TY - JOUR
AU - Rebolledo, Rolando
TI - Decoherence of quantum Markov semigroups
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2005
PB - Elsevier
VL - 41
IS - 3
SP - 349
EP - 373
LA - eng
KW - quantum Markov semigroup; decoherence; limit behaviour; invariant subalgebras
UR - http://eudml.org/doc/77849
ER -

References

top
  1. [1] L. Accardi, Y.G. Lu, I. Volovich, Quantum Theory and its Stochastic Limit, Springer-Verlag, 2002. Zbl1140.81307MR1925437
  2. [2] R. Alicki, K. Lendi, Quantum Dynamical Semigroups and Applications, Lecture Notes in Phys., vol. 286, Springer-Verlag, 1987. Zbl0652.46055MR911678
  3. [3] Ph. Biane, Quelques propriétés du mouvement Brownien non-commutatif. Hommage à P.A. Meyer et J. Neveu, Astérisque236 (1996) 73-102. Zbl0867.46043MR1417975
  4. [4] Ph. Blanchard, R. Olkiewicz, Decoherence induced transition from quantum to classical dynamics, Rev. Math. Phys.15 (2003) 217-243. Zbl1074.81042MR1981622
  5. [5] O. Bratteli, D.W. Robinson, Operator Algebras and Quantum Statistical Mechanics, vol. 1, Springer-Verlag, 1987. Zbl0905.46046MR545651
  6. [6] O. Bratteli, D.W. Robinson, Operator Algebras and Quantum Statistical Mechanics, vol. 2, Springer-Verlag, 1996. Zbl0463.46052
  7. [7] M. Brune et al., Phys. Rev. Lett.77 (1996) 4887. 
  8. [8] A.M. Chebotarev, F. Fagnola, Sufficient conditions for conservativity of minimal quantum dynamical semigroups, J. Funct. Anal.153 (1998) 382-404. Zbl0914.47040MR1614586
  9. [9] A.M. Chebotarev, Lectures on Quantum Probability, Aportaciones Matemáticas, Ser. Textos, vol. 14, Soc. Mat. Mexicana, México, 2000. Zbl1010.60093MR1925129
  10. [10] E. Christensen, D.E. Evans, Cohomology of operator algebras and quantum dynamical semigroups, J. London Math. Soc.20 (1979) 358-368. Zbl0448.46040MR551466
  11. [11] E.B. Davies, Quantum dynamical semigroups and the neutron diffusion equation, Rep. Math. Phys.11 (1977) 169-188. Zbl0372.47020MR503331
  12. [12] C. Dellacherie, P.-A. Meyer, Probabilités et potentiel. Chapitres XII–XVI, Hermann, Paris, 1987. Zbl0624.60084MR898005
  13. [13] G. Dell Antonio, On Decoherence, J. Math. Phys.44 (2003) 4939-4956. Zbl1062.81163MR2014837
  14. [14] F. Fagnola, Quantum Markov semigroups and quantum flows, Proyecciones J. Math.18 (3) (1999) 1-144. Zbl1255.81185MR1814506
  15. [15] F. Fagnola, R. Rebolledo, The approach to equilibrium of a class of quantum dynamical semigroups, Infinite Dimensional Anal. Quantum Probab. Related Topics1 (4) (1998) 1-12. Zbl0923.46073MR1665275
  16. [16] F. Fagnola, R. Rebolledo, On the existence of invariant states for quantum dynamical semigroups, J. Math. Phys.42 (2001) 1296-1308. Zbl1013.81031MR1814690
  17. [17] F. Fagnola, R. Rebolledo, Subharmonic projections for a quantum Markov semigroup, J. Math. Phys.43 (2002) 1074-1082. Zbl1059.47049MR1878987
  18. [18] F. Fagnola, R. Rebolledo, Transience and recurrence of quantum Markov semigroups, Probab. Theory Related Fields126 (2003) 289-306. Zbl1024.60031MR1990058
  19. [19] A. Frigerio, M. Verri, Long-time asymptotic properties of dynamical semigroups on w * -algebras, Math. Z. (1982). Zbl0471.46048
  20. [20] D. Giulini et al., Decoherence and the Appearance of a Classical world in Quantum Theory, Springer, Heidelberg, 1996. Zbl0855.00003
  21. [21] V. Gorini, A. Kossakowski, E.C.G. Sudarshan, Completely positive dynamical semigroups of n-level systems, J. Math. Phys.17 (1976) 821-825. MR406206
  22. [22] A. Holevo, Statistical Structure of Quantum Theory, Lecture Notes in Phys., vol. 67, Springer-Verlag, 2001. Zbl0999.81001MR1889193
  23. [23] T.M. Liggett, Interacting Particle Systems, Springer-Verlag, New York, 1985. Zbl0559.60078MR776231
  24. [24] T.M. Liggett, Stochastic Interacting Systems: Contact, Voter and Exclusion Processes, Springer-Verlag, Berlin, 1999. Zbl0949.60006MR1717346
  25. [25] G. Lindblad, On the generators of quantum dynamical semigroups, Commun. Math. Phys.48 (1976) 119-130. Zbl0343.47031MR413878
  26. [26] A. Majewski, R.F. Streater, Detailed balance and quantum dynamical maps, J. Phys. A31 (1998) 7981-7995. Zbl0929.46060MR1647879
  27. [27] P.-A. Meyer, Quantum Probability for Probabilists, Lecture Notes in Math., vol. 1538, Springer-Verlag, Berlin, 1993. Zbl0773.60098MR1222649
  28. [28] C.J. Myatt et al., Nature403 (2000) 269. 
  29. [29] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, 1983. Zbl0516.47023MR710486
  30. [30] K.R. Parthasarathy, An Introduction to Quantum Stochastic Calculus, Monographs in Math., vol. 85, Birkhaüser, Basel, 1992. Zbl0751.60046MR1164866
  31. [31] W.F. Stinespring, Positive functions on C * -algebras, Proc. Amer. Math. Soc.6 (1955) 211-216. Zbl0064.36703
  32. [32] G.K. Pedersen, Analysis Now, Graduate Texts in Math., vol. 118, Springer-Verlag, 1989. Zbl0668.46002MR971256
  33. [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. MR2012179

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.