Construction of a family of quantum Ornstein-Uhlenbeck semigroups

Chul Ki Ko, Yong Moon Park

Research output: Contribution to journalArticle

5 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)609-627
Number of pages19
JournalJournal of Mathematical Physics
Volume45
Issue number2
DOIs
Publication statusPublished - 2004 Feb 1

Fingerprint

Ornstein-Uhlenbeck Semigroup
algebra
Semigroup
Ornstein-Uhlenbeck process
operators
Hilbert space
generators
Dirichlet Form
Ornstein-Uhlenbeck Process
Eigenspace
Von Neumann Algebra
Elliptic Operator
Dirichlet
Subalgebra
Generator
Algebra
Invariant
Family
Operator

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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Construction of a family of quantum Ornstein-Uhlenbeck semigroups. / Ko, Chul Ki; Park, Yong Moon.

In: Journal of Mathematical Physics, Vol. 45, No. 2, 01.02.2004, p. 609-627.

Research output: Contribution to journalArticle

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