The Green-Kubo formula for the spin-fermion system

Communications in Mathematical Physics

Volumn 268, Issue 2, 2006, Pages 369-401

  Jaksic V ^a   Ogata, Y ^b,c   Pillet, C A ^b  

^a MCGILL UNIVERSITY   (Canada)

^b Univ du Sud   (France)

^c UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33750030537     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-006-0095-0     Document Type: Article

References (44)

1. [Ar] Araki, H.: Relative Hamiltonians for faithful normal states of a von Neumann algebra. Publ. R.I.M.S., Kyoto Univ. 9, 165 (1973)
2. [AH] Araki, H., Ho, T.G: Asymptotic time evolution of a partitioned infinite two-sided Isotropic XY-chain. Tr. Mat. Inst. Steklova, 228 Probl. Sovrem. Mat. Fiz., 203 (2000);
3. translation in Proc. Steklov Inst. Math. 228, 191 (2000)
4. [AP] Aschbacher, W., Pillet, C-A.: Non-equilibrium steady states of the XY chain. J. Stat. Phys. 12, 1153 (2003)
5. [AJPP1] Aschbacher, W., Jakšić, V., Pautrat, Y. Pillet, C.-A.: Topics in non-equilibrium quantum statistical mechanics. In: Open Quantum Systems III. Attal, S., Joye, A., Pillet, C.-A. (eds) Lecture Notes in Mathematics 1882, New York: Springer, New York 2006
6. [AJPP2] Aschbacher, W., Jakšić, V., Pautrat, Y., Pillet, C.-A.: Transport properties of ideal Fermi gases. (In preparation)
7. [AW] Araki, H., Wyss, W.: Representations of canonical anti-commutation relations. Helv. Phys. Acta 37, 136 (1964)
8. [BFS] Bach, V., Fröhlich, J., Sigal, I.: Return to equilibrium. J. Math. Phys. 41, 3985 (2000)
9. [BGKS] Bouclet, J.M., Germinet, F., Klein, A., Schenker, J.H.: Linear response theory for magnetic Schrödinger operators in disordered media. J. Funct. Anal. 226, 301-372 (2005)
10. [BRI] Bratteli, O., Robinson, D. W.: Operator Algebras and Quantum Statistical Mechanics 1. Berlin: Springer-Verlag 1987
11. [BR2] Bratteli, O., Robinson, D. W.: Operator Algebras and Quantum Statistical Mechanics 2. Second edition, Berlin: Springer-Verlag, (1996)
12. [Da] Davies, E.B.: Markovian master equations. Commun. Math. Phys. 39, 91 (1974)
13. [De] Dereziński, J.: Fermi Golden Rule and open quantum systems. In: Open Quantum Systems III Attal, S., Joye, A., Pillet, C.-A. (eds) Lecture Notes in Mathematics 1882, New York: Springer 2006
14. [DJ1] Dereziński, J., Jakšić, V.: On the nature of Fermi Golden Rule for open quantum systems. J. Stat. Phys. 116, 411 (2004)
15. [DJ] Dereziński, J., Jakšić, V.: Return to equilibrium for Pauli-Fierz systems. Ann. Henri Poincaré 4, 739 (2003)
16. [DJP] Dereziński, J., Jakšić, V., Pillet, C.-A. : Perturbation theory of W*-dynamics, KMS-states and Liouvilleans. Rev. Math. Phys. 15, 447 (2003)
17. [FM] Fröhlich, J., Merkli, M.: Another return of return to equilibrium. Commun. Math. Phys. 251, 235 (2004)
18. [FMU] Fröhlich, J., Merkli, M., Ueltschi, D.: Dissipative transport: thermal contacts and tunneling junctions. Ann. Henri Poincaré 4, 897 (2004)
19. [GW] Goderis, D., Verbeure, A., Vets, P.: About the exactness of the linear response theory. Commun. Math. Phys. 136, 265 (1991)
20. [JOP1] Jakšić, V., Ogata, Y., Pillet, C.-A.: The Green-Kubo formula and the Onsager reciprocity relations in quantum statistical mechanics. Commun. Math. Phys. 265(3), 721-738 (2006)
21. [JOP2] Jakšić, V., Ogata, Y., Pillet, C.-A.: Linear response theory for thermally driven open quantum systems. To appear in J. Stat. Phys. DOI:10.1007/s10955-006-9075-1
22. [JOPR] Jakšić, V., Ogata, Y., Pillet, C.-A.: The Evans-Searles symmetry for classical and quantum dynamical systems. In preparation
23. [JP1] Jakšić, V., Pillet, C-A.: On a model for quantum friction II. Fermi's golden rule and dynamics at positive temperature. Commun. Math. Phys. 176, 619 (1996)
24. [JP2] Jakšić, V., Pillet, C.-A.: On entropy production in quantum statistical mechanics. Commun. Math. Phys. 217, 285 (2001)
25. [JP3] Jakšić, V., Pillet, C.-A.: Non-equilibrium steady states for finite quantum systems coupled to thermal reservoirs. Commun. Math. Phys. 226, 131 (2002)
26. [JP4] Jakšić, V., Pillet, C.-A.: Mathematical theory of non-equilibrium quantum statistical mechanics. J. Stat. Phys. 108, 787 (2002)
27. [JP5] Jakšić, V., Pillet, C.-A.: A note on the entropy production formula. Contemp. Math. 327, 175 (2003)
28. [JP6] Jakšić, V., Pillet, C.-A.: On a model for quantum friction III: Fjrgodic properties of the spin-boson system. Commun. Math. Phys. 178, 627 (1996)
29. [JP7] Jakšić, V., Pillet, C.-A.: In preparation.
30. [KTH] Kubo, R., Toda, M., Hashitsune, N.: Statistical Physics II. Second edition, Berlin: Springer-Verlag 1991
31. [LeSp] Lebowitz, J., Spohn, H.: Irreversible thermodynamics for quantum systems weakly coupled to thermal reservoirs. Adv. Chem. Phys. 39, 109 (1978)
32. [M] MacLennan, J.A.: Adv. Chem. Phys. 5, 261 (1963)
33. [MMS] Merkli, M., Mueck, M., Sigal, I.M.: Instability of equilibrium states for coupled heat reservoirs at different temperatures, http://arxiv.org/list/math-ph/0508005, 2005
34. [NVW] Naudts, J., Verbeure, A., Weder, R.: Linear response theory and the KMS condition. Commun. Math. Phys. 44, 87 (1975)
35. [RBT] Rey-Bellet, L., Thomas, L.E.: Fluctuations of the entropy production in anharmonic chains. Ann. Henri Poinc. 3, 483 (2002)
36. [Ru1] Ruelle, D.: Natural nonequilibrium states in quantum statistical mechanics. J. Stat. Phys. 98, 57 (2000)
37. [Ru2] Ruelle, D.: Entropy production in quantum spin systems. Commun. Math. Phys. 224, 3 (2001)
38. [Ru3] Ruelle, D.: Topics in quantum statistical mechanics and operator algebras. http://arxiv.org/list/math-ph/0107009, 2001
39. [Si] Simon, B.: Fifteen problems in mathematical physics. Perspectives in mathematics, 423, Basel: Birkhäuser (1984)
40. [Sp] Spohn, H.: An algebraic condition for the approach to equilibrium of an open N-level system. Lett. Math. Phys. 2, 33 (1977)
41. [TM] Tasaki, S., Matsui, T.: Fluctuation theorem, nonequilibrium steady states and MacLennan-Zubarev ensembles of a class of large quantum systems. In: Fundamental Aspects of Quantum Physics (Tokyo, 2001). QP-PQ: Quantum Probab. White Noise Anal., 17, River Edge, NJ: World Sci., 2003, p. 100
42. [Zu] Zubarev, D.N.: Nonequilibrium statistical thermodynamics. NY: Consultant Bureau 1974
43. [ZMR1] Zubarev, D. N., Morozov, V. G., Röpke, G.: Statistical Mechanics of Nonequilibrium Processes I. Berlin: Academie Verlag 1996
44. [ZMR2] Zubarev, D. N., Morozov, V. G., Röpke, G.: Statistical Mechanics of Nonequilibrium Processes II. Berlin: Academie Verlag 1997