Markov states and chains on the car algebra

Infinite Dimensional Analysis, Quantum Probability and Related Topics

Volumn 10, Issue 2, 2007, Pages 165-183

  Accardi, Luigi ^a   Fidaleo, Francesco ^a   Mukhamedov, Farruh ^b  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

^b NATIONAL UNIVERSITY OF UZBEKISTAN   (Uzbekistan)

Author keywords

Integration and probability; Mathematical quantum statistical mechanics; Noncommutative measure; Quantum Markov processes

Indexed keywords

EID: 34250191126     PISSN: 02190257     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219025707002683     Document Type: Article

References (22)

1. L. Accardi, Noncommutative Markov chains, in Proc. of Int. School of Math. Phys., Camerino (1974), pp. 268-295.
2. L. Accardi, On noncommutative Markov property, Funct. Anal. Appl. 8 (1975) 1-8.
3. L. Accardi and C. Cecchini, Conditional expectations in von Neumann algebras and a theorem of Takesaki, J. Funct. Anal. 45 (1982) 245-273.
4. L. Accardi and F. Fidaleo, Nonhomogeneous quantum Markov states and quantum Markov fields, J. Funct. Anal. 200 (2003) 324-347.
5. L. Accardi and F. Fidaleo, Quantum Markov fields, Inf. Dim. Anal. Quantum Probab. Rel. Topics 6 (2003) 123-138.
6. L. Accardi and F. Fidaleo, Entangled Markov chains, Ann. Mat. Pura Appl. 184 (2005) 327-346.
7. L. Accardi and A. Frigerio, Markovian cocycles, Proc. R. Ir. Acad. 83 (1983) 251-263.
8. L. Accardi and V. Liebscher, Markovian KMS states for one dimensional spin chains, Inf. Dim. Anal. Quantum Probab. Rel. Topics 2 (1999), 645-661.
9. H. Araki and H. Moriya, Local thermodynamical stability of Fermion lattice systems, Lett. Math. Phys. 62 (2002) 33-45.
10. H. Araki and H. Moriya, Equilibrium statistical mechanics of Fermion lattice systems, Rev. Math. Phys. 15 (2003) 93-198.
11. H. Araki and H. Moriya, Joint extension of states of subsystems, Commun. Math. Phys. 237 (2003) 105-122.
12. H. Araki, Conditional expectations relative to a product state and the corresponding standard potentials, Commun. Math. Phys. 246 (2004) 113-132.
13. O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics, Vols. I and II (Springer, 1981).
14. M. Fannes, B. Nachtergaele and R. F. Werner, Finitely correlated states of quantum spin chains, Commun. Math. Phys. 144 (1992) 443-490.
15. M. Fannes, B. Nachtergaele and R. F. Werner, Finitely correlated pure states, J. Funct. Anal. 120 (1994) 511-534.
16. F. Fidaleo and F. Mukhamedov, Diagonalizability of nonhomogeneous quantum Markov states and associated von Neumann algebras, Probab. Math. Stat. 24 (2004) 401-418.
17. Ya V. Golodets and G. N. Zholtkevich, Markovian KMS states, Theor. Math. Phys. 56 (1983) 686-690.
18. F. Hiai and D. Petz, Entropy densities for algebraic states, J. Funct. Anal. 125 (1994) 287-308.
19. T. Matsui, A characterization of pure finitely correlated states, Inf. Dim. Anal. Quantum Probab. Rel. Topics 1 (1998) 647-661.
20. H. Ohno, Extendability of generalized quantum Markov states on gauge invariant C*-algebras, Inf. Dim. Anal. Quantum Probab. Rel. Topics 8 (2005) 141-152.
21. D. Petz, Monotonicity of quantum relative entropy revisited, Rev. Math. Phys. 15 (2003) 79-91.
22. M. Takesaki, Theory of Operator Algebras I (Springer, 1979).