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A FAMILY OF QUANTUM MARKOV SEMIGROUPS
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 Title & Authors
A FAMILY OF QUANTUM MARKOV SEMIGROUPS
Ahn, Sung-Ki; Ko, Chul-Ki; Pyung, In-Soo;
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 Abstract
For a given gauge invariant state on the CAR algebra A isomorphic with the C -algebra of complex matrices, we construct a family of quantum Markov semigroups on A which leave w invariant. By analyzing their generators, we decompose the algebra A into four eigenspaces of the semigroups and show some properties.
 Keywords
quantum Markov semigroups;quasi-free states;CAR algebras;
 Language
English
 Cited by
 References
1.
G. Alii and G. L. Sewell, New method and structures in the theory of the multimode Dicke laser model, J. Math. Phys. 36 (1995), no. 10, 5598-5626 crossref(new window)

2.
C. Bahn and C. K. Ko, Construction of unbounded Dirichlet forms on standard forms of von Neumann Algebras, J. Korean Math. Soc. 39 (2002), no. 6, 931-951 crossref(new window)

3.
C. Bahn, C. K. Ko, and Y. M. Park, Dirichlet forms and symmetric Markovian semigroups on CCR Algebras with quasi-free states, J. Math. Phys. 44 (2003), 723-753 crossref(new window)

4.
C. Bahn, C. K. Ko, and Y. M. Park, Construction of symmetric Markovian semigroups on standard forms of $Z_2$-graded von Neumann Algebras, Rev. Math. Phys. 15 (2003), 823-845 crossref(new window)

5.
C. Bahn and Y. M. Park, Feynman Kac representation and Markov property of semigroups generated by noncommutative elliptic operators, Infin. Dimens Anal. Quantum Probab. Relat. Top. 6 (2003), no. 1, 103-121

6.
O. Bratteli and D. W. Robinson, Operator algebras and quantum statistical mechanics, 2nd Edition, Springer-Verlag, New York-Heidelberg-Berlin, vol I 1987, vol. II 1997

7.
F. Cipriani, Dirichlet forms and Markovian semigroups on standard forms of von Neumann algebras, J. Funct. Anal. 147 (1997), 259-300 crossref(new window)

8.
E. B. Davies, Quantum theory of open systems, Academic Press, London-New York-San Francisco, 1976

9.
E. B. Davies and J. M. Lindsay, Superderivations and symmetric Markov semigroups, Comm. Math. Phys. 157 (1993), 359-370 crossref(new window)

10.
C. K. Ko and Y. M. Park, Construction of a Family of Quantum OrnsteinUhlenbeck Semigroups, J. Math. Phys. 45 (2004) 609-627 crossref(new window)

11.
A. Luczak, Mixing and asymptotic properties of Markov semigroups on von Neumann algebras, Math. Z. 235 (2000) 615-626 crossref(new window)

12.
A. W. Majewski and B. Zegarlinski, Quantum stochastic dynamics I: Spin systems on a lattice, Math. Phys. Electron. J. 1 (1995)

13.
A. W. Majewski and B. Zegarlinski, Quantum. stochastic dynamics II, Rev. Math. Phys. 8 (1996), 689-713 crossref(new window)

14.
Y. M. Park, Construction of Dirichlet forms and standard forms of von Neumann algebras, Infin. Dimens Anal. Quantum Probab. Relat. Top, 3 (2000), 1-14 crossref(new window)

15.
K. R. Parthasarathy, An introduction to quantum stochastic calculus, Birkhauser, Basel (1992)

16.
I. E. Segal, A non-commutative extension of abstract integration, Ann. of Math. 57 (1953), 401-456 crossref(new window)