Abstract
Examples of the theory of stochastic calculus on local algebras ([Ac Pa 1], [Ac Pa 2]) are constructed using a wide class of quasi-free states on the CCR and CAR algebras (see also [Ba St Wi] for a complementary analysis). Having established, in each case, the appropriate rule for multiplication of stochastic differentials, we investigate a class of stochastic differential equations whose solution is a family of unitary operators on an appropriate Hilbert space. We thus obtain a technique for constructing unitary dilations of a certain class of completely positive evolutions which generalises the unitary dilation scheme for quantum dynamical semigroups which have been constructed using the Fock state ([Hu Pa], [Ap Hu]) and extremal universally invariant (e.u.i.) quasi-free states [Hu Li].
Work begun when the author was supported by a CNR Visiting Professorship and completed when supported by an SERC European Fellowship.
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References
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© 1985 Springer-Verlag
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Applebaum, D. (1985). Quasi-free stochastic evolutions. In: Accardi, L., von Waldenfels, W. (eds) Quantum Probability and Applications II. Lecture Notes in Mathematics, vol 1136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074458
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DOI: https://doi.org/10.1007/BFb0074458
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