The classical limit of reduced quantum stochastic evolutions
Annales de l'I.H.P. Physique théorique, Tome 43 (1985) no. 2, pp. 133-145.
@article{AIHPA_1985__43_2_133_0,
     author = {Hudson, Robin and Lindsay, Martin},
     title = {The classical limit of reduced quantum stochastic evolutions},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {133--145},
     publisher = {Gauthier-Villars},
     volume = {43},
     number = {2},
     year = {1985},
     mrnumber = {817531},
     zbl = {0581.60067},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPA_1985__43_2_133_0/}
}
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
SP  - 133
EP  - 145
VL  - 43
IS  - 2
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPA_1985__43_2_133_0/
LA  - en
ID  - AIHPA_1985__43_2_133_0
ER  - 
%0 Journal Article
%A Hudson, Robin
%A Lindsay, Martin
%T The classical limit of reduced quantum stochastic evolutions
%J Annales de l'I.H.P. Physique théorique
%D 1985
%P 133-145
%V 43
%N 2
%I Gauthier-Villars
%U http://archive.numdam.org/item/AIHPA_1985__43_2_133_0/
%G en
%F AIHPA_1985__43_2_133_0
Hudson, Robin; Lindsay, Martin. The classical limit of reduced quantum stochastic evolutions. Annales de l'I.H.P. Physique théorique, Tome 43 (1985) no. 2, pp. 133-145. http://archive.numdam.org/item/AIHPA_1985__43_2_133_0/

[1] L. Accardi, A. Frigerio and J.T. Lewis, Quantum stochastic processes Publ. R. I. M. S., t. 18, 1982, p. 97-133. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[4] J.M. Bismut, Mécanique aléatoire. Lecture Notes in Mathematics, t. 866. Springer-Verlag, 1981. | MR | Zbl

[5] O. Bratteli and D.W. Robinson, Operator algebras and quantum statistical mechanics. Springer-Verlag, 1981. | MR | Zbl

[6] A.M. Cockroft and R.L. Hudson, Quantum mechanical Wiener processes. J. Multivariate Anal., t. 7, 1977, p. 107-124. | MR | Zbl

[7] E.B. Davies, The classical limit for quantum dynamical semigroups. Commun. Mat. Phys., t. 49, 1976, p. 113-129. | MR | Zbl

[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. | MR

[9] K. Hepp, The classical limit for quantum-mechanical correlation functions. Commun. Math. Phys., t. 35, 1974, p. 265-277. | MR

[10] R.L. Hudson and K.R. Parthasarathy, Quantum Ito's formula and stochastic evolutions. Commun. Math. Phys., t. 93, 1984, p. 301-323. | MR | Zbl

[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. | MR | Zbl

[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. | Zbl

[12b] J.M. Lindsay, PhD Thesis, Nottingham, 1985.

[13] N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes. North-Holland, 1981. | MR | Zbl

[14] D. Kastler, The C*-algebra of a free Boson field. Commun. Math. Phys., t. 1, 1965, p. 14-48. | MR | Zbl

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

[16] J.E. Moyal, Quantum mechanics as a statistical theory. Proc. Camb. Phil. Soc., t. 45, 1949, p. 99-124. | MR | Zbl

[17] J. Von Neumann, Die Eindeutigkeit der Schrödingerden Operatoren. Math. Ann., t. 104, 1931, p. 570-578. | JFM | MR | Zbl

[18] M. Takesaki, Conditional expectations in von Neumann algebras. J. Funct. Anal., t. 9, 1972, p. 306-321. | MR | Zbl

[19] H. Weyl, The theory of groups and quantum mechanics (tr. Robertson H. P.). Dover, New York, 1950. | Zbl

[20] E.P. Wigner, On the quantum correction for thermodynamic equilibrium. Phys. Rev., t. 40, 1932, p. 749-759. | JFM | Zbl