Non-Equilibrium Steady States of the XY Chain

Journal of Statistical Physics

Volumn 112, Issue 5-6, 2003, Pages 1153-1175

  Aschbacher, Walter H ^a   Pillet, Claude Alain ^b  

^a UNIVERSITÉ DE TOULON   (France)

^b Aix Marseille University   (France)

Author keywords

Bogoliubov automorphism; Jordan Wigner transformation; Non equilibrium steady state; Scattering theory; XY chain

Indexed keywords

EID: 0037829570     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1024619726273     Document Type: Article

References (31)

1. H. Araki, On the XY-model on two-sided infinite chain, Publ. RIMS Kyoto Univ. 20:277-296 (1984).
2. H. Araki, Master symmetries of the XY model, Comm. Math. Phys. 132:155-176 (1990).
3. H. Araki, On quasifree states of CAR and Bogoliubov automorphisms, Publ. RIMS Kyoto Univ. 6:385-442 (1971).
4. A. Y. Alekseev, V. V. Cheianov, and J. Fröhlich, Universality of transport properties in equilibrium, the goldstone theorem and chiral anomaly, Phys. Rev. Lett. 81:3503-3506 (1998).
5. H. Araki and E. Barouch, On the dynamics and ergodic properties of the XY model, J. Stat. Phys. 31:327-345 (1983).
6. H. Araki and T. G. Ho, Asymptotic time evolution of a partitioned infinite two-sided isotropic XY-chain, Proc. Steklov Inst. Math. 228:191-204 (2000).
7. E. Barouch and B. Fuchssteiner, Master symmetries and similarity equation, Stud. Appl. Math. 73:221-237 (1985).
8. E. Barouch and B. M. McCoy, Statistical mechanics of the XY model II. Spin-correlation functions, Phys. Rev. A 3:786-804 (1971).
9. O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics 1 (Springer, New York, 1987).
10. O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics 2 (Springer, New York, 1997).
11. H. Castella, X. Zotos, and P. Prelovšek, Integrability and ideal conductance at finite temperatures, Phys. Rev. Lett. 74:972-975 (1995).
12. E. B. Davies and B. Simon, Scattering theory for systems with different spatial asymptotics on the left and right, Comm. Math. Phys. 63:277-301 (1978).
13. S. Dirren and J. Fröhlich, Unpublished.
14. L. Hume and D. W. Robinson, Return to equilibrium in the XY model, J. Stat. Phys. 44:829-848 (1986).
15. V. Jakšić and C.-A. Pillet, On entropy production in quantum statistical mechanics, Comm. Math. Phys. 217:285-293 (2001).
16. V. Jakšić and C.-A. Pillet, Mathematical theory of non-equilibrium quantum statistical mechanics, J. Stat. Phys. 108:787 (2002).
17. V. Jakšić and C.-A. Pillet, A note on the entropy production formula. To appear in Contemp. Math.
18. P. Jordan and E. Wigner, Pauli's equivalence prohibition, Z. Phys. 47: 631 (1928).
19. E. Lieb, T. Schultz, and D. Mattis, Two soluble models of an antiferromagnetic chain, Ann. Physics 16:407-466 (1961).
20. T. Matsui, On conservation laws of the XY model, Math. Phys. Stud. 16:197-204 (1993).
21. B. M. McCoy, Spin correlation functions of the XY model, Phys. Rev 173:531-541 (1968).
22. Y. Nambu, A note on the eigenvalue problem in crystal statistics, Progr. Theor. Phys. Japan 5:1-13 (1950).
23. M. Reed and B. Simon, Methods of Modern Mathematical Physics III: Scattering Theory (Academic Press, New York, 1979).
24. D. Ruelle, Entropy production in quantum spin systems, Comm. Math. Phys. 224:3-16 (2001).
25. D. Ruelle, Natural nonequilibrium states in quantum statistical mechanics, J. Stat. Phys. 98:57-75 (2000).
26. K. Saito, S. Takesue, and S. Miyashita, Thermal conduction in a quantum system, Phys. Rev. E 54:2404-2408 (1996).
27. S. Sakai, C*-Algebras and W*-Algebras (Springer, New York, 1971).
28. 3, Phys. Rev. B 64 (2001), 054412-1-054412-11.
29. 3: Evidence for the thermal transport via spinons, Phys. Rev. B 62:R6108-R6111 (2000).
30. X. Zotos, Finite temperature Drude weight of the one-dimensional spin-1/ 2 Heisenberg model, Phys. Rev. Lett. 82:1764-1767 (1999).
31. X. Zotos, F. Naef, and P. Prelovšek, Transport and conservation laws, Phys. Rev. B 55:11029-11032 (1997).