Abstract
Employing the construction method of Dirichlet forms on standard forms of von Neumann algebras developed in Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2000, Vol. 3, No. 1, pp. 1-14 (Ref. 1), we construct Dirichlet forms and associated symmetric Markovian semigroups on CCR algebras with respect to quasi-free states. More precisely, let A(Heng hooktop sign0) be the CCR algebra over a complex separable pre-Hilbert space Heng hooktop sign0 and let ω be a quasi-free state on A(Heng hooktop sign0). For any normalized admissible function f and complete orthonormal system (CONS) {gn}Heng hooktop sign0, we construct a Dirichlet form and corresponding symmetric Markovian semigroup on the natural standard form associated to the GNS representation of (A(Heng hooktop sign0), ω). It turns out that the form is independent of admissible function f and CONS {gn} chosen. By analyzing the spectrum of the generator (Dirichlet operator) of the semigroup, we show that the semigroup is ergodic and tends to the equilibrium exponentially fast.
| Original language | English |
|---|---|
| Pages (from-to) | 723-753 |
| Number of pages | 31 |
| Journal | Journal of Mathematical Physics |
| Volume | 44 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2003 Feb 1 |
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All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
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Dirichlet forms and symmetric Markovian semigroups on CCR algebras with respect to quasi-free states. / Bahn, Changsoo; Ko, Chul Ki; Park, Yong Moon.
In: Journal of Mathematical Physics, Vol. 44, No. 2, 01.02.2003, p. 723-753.Research output: Contribution to journal › Article
TY - JOUR
T1 - Dirichlet forms and symmetric Markovian semigroups on CCR algebras with respect to quasi-free states
AU - Bahn, Changsoo
AU - Ko, Chul Ki
AU - Park, Yong Moon
PY - 2003/2/1
Y1 - 2003/2/1
N2 - Employing the construction method of Dirichlet forms on standard forms of von Neumann algebras developed in Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2000, Vol. 3, No. 1, pp. 1-14 (Ref. 1), we construct Dirichlet forms and associated symmetric Markovian semigroups on CCR algebras with respect to quasi-free states. More precisely, let A(Heng hooktop sign0) be the CCR algebra over a complex separable pre-Hilbert space Heng hooktop sign0 and let ω be a quasi-free state on A(Heng hooktop sign0). For any normalized admissible function f and complete orthonormal system (CONS) {gn}Heng hooktop sign0, we construct a Dirichlet form and corresponding symmetric Markovian semigroup on the natural standard form associated to the GNS representation of (A(Heng hooktop sign0), ω). It turns out that the form is independent of admissible function f and CONS {gn} chosen. By analyzing the spectrum of the generator (Dirichlet operator) of the semigroup, we show that the semigroup is ergodic and tends to the equilibrium exponentially fast.
AB - Employing the construction method of Dirichlet forms on standard forms of von Neumann algebras developed in Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2000, Vol. 3, No. 1, pp. 1-14 (Ref. 1), we construct Dirichlet forms and associated symmetric Markovian semigroups on CCR algebras with respect to quasi-free states. More precisely, let A(Heng hooktop sign0) be the CCR algebra over a complex separable pre-Hilbert space Heng hooktop sign0 and let ω be a quasi-free state on A(Heng hooktop sign0). For any normalized admissible function f and complete orthonormal system (CONS) {gn}Heng hooktop sign0, we construct a Dirichlet form and corresponding symmetric Markovian semigroup on the natural standard form associated to the GNS representation of (A(Heng hooktop sign0), ω). It turns out that the form is independent of admissible function f and CONS {gn} chosen. By analyzing the spectrum of the generator (Dirichlet operator) of the semigroup, we show that the semigroup is ergodic and tends to the equilibrium exponentially fast.
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UR - http://www.scopus.com/inward/citedby.url?scp=0037326790&partnerID=8YFLogxK
U2 - 10.1063/1.1532770
DO - 10.1063/1.1532770
M3 - Article
AN - SCOPUS:0037326790
VL - 44
SP - 723
EP - 753
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
SN - 0022-2488
IS - 2
ER -