The classical limit of reduced quantum stochastic evolutions

Robin Hudson; Martin Lindsay

Annales de l'I.H.P. Physique théorique (1985)

  • Volume: 43, Issue: 2, page 133-145
  • ISSN: 0246-0211

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Hudson, Robin, and Lindsay, Martin. "The classical limit of reduced quantum stochastic evolutions." Annales de l'I.H.P. Physique théorique 43.2 (1985): 133-145. <http://eudml.org/doc/76294>.

@article{Hudson1985,
author = {Hudson, Robin, Lindsay, Martin},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {quantum stochastic evolutions; infinitesimal generators; quantum diffusions; semi-elliptic differential operators},
language = {eng},
number = {2},
pages = {133-145},
publisher = {Gauthier-Villars},
title = {The classical limit of reduced quantum stochastic evolutions},
url = {http://eudml.org/doc/76294},
volume = {43},
year = {1985},
}

TY - JOUR
AU - Hudson, Robin
AU - Lindsay, Martin
TI - The classical limit of reduced quantum stochastic evolutions
JO - Annales de l'I.H.P. Physique théorique
PY - 1985
PB - Gauthier-Villars
VL - 43
IS - 2
SP - 133
EP - 145
LA - eng
KW - quantum stochastic evolutions; infinitesimal generators; quantum diffusions; semi-elliptic differential operators
UR - http://eudml.org/doc/76294
ER -

References

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  2. [2] W. Arveson, Quantisation and the uniqueness of invariant structures. Commun. Math. Phys., t. 89, 1983, p. 77-102 and Addendum, t. 93, 1984, p. 141. Zbl0522.58022MR707773
  3. [3] F. Bayen, M. Flato, C. Fronsdal, A. Lichnerovicz and D. Sternheimer, Deformation theory and Quantisation. I Deformations of symplectic structures. II Physical applications. Annals of Physics, t. 111, 1978, p. 61-110 and p. 111-151. Zbl0377.53024MR496157
  4. [4] J.M. Bismut, Mécanique aléatoire. Lecture Notes in Mathematics, t. 866. Springer–Verlag, 1981. Zbl0457.60002MR629977
  5. [5] O. Bratteli and D.W. Robinson, Operator algebras and quantum statistical mechanics. Springer-Verlag, 1981. Zbl0463.46052MR611508
  6. [6] A.M. Cockroft and R.L. Hudson, Quantum mechanical Wiener processes. J. Multivariate Anal., t. 7, 1977, p. 107-124. Zbl0401.60086MR450495
  7. [7] E.B. Davies, The classical limit for quantum dynamical semigroups. Commun. Mat. Phys., t. 49, 1976, p. 113-129. Zbl0355.60069MR468873
  8. [8] A. Frigerio and V. Gorini, Diffusion processes, quantum dynamical semigroups and the classical K. M. S. condition. J. Math. Phys., t. 25, 1984, p. 1050-1065. MR739262
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  11. [11] R.L. Hudson and J.M. Lindsay, A non-commutative martingale representation theorem for non-Fock quantum Brownian motion. J. Funct. Anal., t. 61, 1985, p. 202-221. Zbl0577.60055MR786622
  12. [12a] R.L. Hudson and J.M. Lindsay, Uses of non-Fock quantum Brownian motion and a martingale representation theorem. To appear in the Proceedings of the 2nd workshop on Quantum Probability and Applications, 1984. Ed. Accardi L. et al. Lecture Notes in Mathematics. Zbl0569.60055
  13. [12b] J.M. Lindsay, PhD Thesis, Nottingham, 1985. 
  14. [13] N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes. North-Holland, 1981. Zbl0495.60005MR637061
  15. [14] D. Kastler, The C*-algebra of a free Boson field. Commun. Math. Phys., t. 1, 1965, p. 14-48. Zbl0137.45601MR193983
  16. [15] G. Lindblad, On the generators of quantum dynamical semigroups. Commun. Math. Phys., t. 48, 1976, p. 119-130. Zbl0343.47031MR413878
  17. [16] J.E. Moyal, Quantum mechanics as a statistical theory. Proc. Camb. Phil. Soc., t. 45, 1949, p. 99-124. Zbl0031.33601MR29330
  18. [17] J. Von Neumann, Die Eindeutigkeit der Schrödingerden Operatoren. Math. Ann., t. 104, 1931, p. 570-578. Zbl0001.24703MR1512685JFM57.1446.01
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