- 03-141 Chul Ki Ko, Yong Moon Park
- Construction of a Family of Quantum Ornstein-Uhlenbeck Semigroups
(427K, Postscript)
Mar 28, 03
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Abstract. For a given quasi-free state on the CCR algebra over one
dimensional Hilbert space, a family of Markovian semigroups which
leave the quasi-free state invariant is constructed by means of
noncommutative elliptic operators and Dirichlet forms on von
Neumann algebras. The generators (Dirichlet operators) of the
semigroups are analyzed and the spectrums together with
eigenspaces are found. When restricted to a maximal abelian
subalgebra, the semigroups are reduced to a unique Markovian
semigroup of classical Ornstein-Uhlenbeck process.
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