Chul Ki Ko, Yong Moon Park
Construction of a Family of Quantum Ornstein-Uhlenbeck Semigroups
(427K, Postscript)

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.