Abstract
Quantum diffusions on the algebra B(ℋ0) of all bounded operators on a Hilbert space are analysed. When ℋ0 is finite dimensional all such diffusions are described by unitary processes. When ℋ0 is infinite dimensional the general such diffusion is shown to be a unitary perturbation, which can be constructed explicitly, of a class of quantum diffusions completely characterised by an endomorphism of B(ℋ0).
Work partly supported by SERC grant GR/D51292 and completed when the author was visiting the University of Strasbourg, whose hospitality is gratefully acknowledged.
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References
M Evans, Existence of quantum diffusions, submitted to Modern Probability and its Applications.
M Evans and R L Hudson, Multidimensional quantum diffusions, in Quantum Probability III, Oberwolfach (1987) Proceedings, ed L Accardi and W von Waldenfels, Springer LNM 1303 (1988).
R L Hudson, Algebraic theory of quantum diffusions, to appear in Swansea (1986) Proceedings, ed A Truman.
R L Hudson, Quantum diffusions and cohomology of algebras, in Proceedings of First World Congress of Bernoulli Society, Vol 1, ed Yu Prohorov and V V Sazonov, pp 479–485 (1987).
R L Hudson and K R Parthasarathy, Quantum Ito's formula and stochastic evolutions, Commun Math Phys, 93, 301–323 (1984).
R V Kadison and J R Ringrose, Fundamentals of the theory of operator algebras Volume 1, Academic Press (1983), Volume 2, Academic Press (1986).
R V Kadison and J R Ringrose, Cohomology of operator algebras I, Acta Math, 126, 227–243 (1971).
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© 1989 Springer-Verlag
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Hudson, R. (1989). Quantum diffusions on the algebra of all bounded operators on a hilbert space. In: Accardi, L., von Waldenfels, W. (eds) Quantum Probability and Applications IV. Lecture Notes in Mathematics, vol 1396. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083556
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DOI: https://doi.org/10.1007/BFb0083556
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