Non-equilibrium steady states of finite quantum systems coupled to thermal reservoirs

Communications in Mathematical Physics

Volumn 226, Issue 1, 2002, Pages 131-162

  Jaksic V ^a   Pillet, C A ^b,c  

^a MCGILL UNIVERSITY   (Canada)

^b UNIVERSITÉ DE TOULON   (France)

^c CENTRE DE PHYSIQUE THÉORIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036002932     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200200602     Document Type: Article

References (36)

1. [Ar1] Araki, H.: Relative entropy of states of von Neumann algebras. Pub. R.I.M.S., Kyoto Univ. 11, 809 (1976)
2. [Ar2] Araki, H.: Relative entropy of states of von Neumann algebras II. Pub. R.I.M.S., Kyoto Univ. 13, 173 (1977)
3. [AW] Araki, H., Wyss, W.: Representations of canonical anticommutation relations. Helv. Phys. Acta 37, 136 (1964)
4. [BSZ] Baez, J.C., Segal, I.E., Zhou, Z.: Introduction to Algebraic and Constructive Quantum Field Theory. Princeton, NJ: Princeton University Press, 1991
5. [BFS] Bach, V., Fröhlich, J., Sigal, I.: Return to equilibrium. J. Math. Phys. 41, 3985 (2000)
6. [BR1] Brattelli, O., Robinson, D.W.: Operator Algebras and Quantum Statistical Mechanics 1. Berlin: Springer-Verlag, Second edition, 1987
7. [BR2] Brattelli, O., Robinson, D.W.: Operator Algebras and Quantum Statistical Mechanics 2. Berlin: Springer-Verlag, Second edition, 1996
8. [Da] Davies, E.B.: Markovian master equations. Commun. Math. Phys. 39, 91 (1974)
9. [Don] Donald, M.J.: Relative Hamiltonians which are not bounded from above. J. Func. Anal. 91, 143 (1990)
10. [DG1] Derezinski, J., Gerard, C.: Asymptotic completeness in quantum field theory. Massive Pauli-Fierz Hamiltonians. Rev. Math. Phys. 11, 383 (2000)
11. 2 Hamiltonians. Commun. Math. Phys. 213, 39 (2000)
12. [DJ1] Derezinski, J., Jakšić, V.: Spectral theory of Pauli-Fierz operators. J. Func. Anal. 180, 243 (2001)
13. [DJ2] Derezinski, J., Jakšić, V.: Return to equilibrium for Pauli-Fierz systems. Submitted
14. [DJP] Derezinski, J., Jakšić, V., Pillet, C.-A.: Perturbation theory of KMS-states. Preprint
15. [Fr] Frigerio, A.: Quantum dynamical semigroups and approach to equilibrium. Lett. Math. Phys. 2, 79 (1977)
16. [FGS] Fröhlich, J., Griesmer, M., Schlein, B.: Asymptotic completeness for Rayleigh scattering. Preprint
17. [GFV] Gorini, V., Frigerio, A., Verri, M., Kossakowski, A., Sudarshan, E.C.G.: Properties of quantum Markovian master equations. Rep. Math. Phys. 13, 149 (1978)
18. [Ha] Haag, R.: Local Quantum Physics. Berlin: Springer-Verlag, 1993
19. [Hak] Haake, F.: Statistical treatment of open systems by generalized master equations. Springer Tracts in Modern Physics 66. Berlin: Springer-Verlag, 1973
20. [HP] Hunziker, W., Pillet, C-A.: Degenerate asymptotic perturbation theory. Commun. Math. Phys. 90, 219 (1983)
21. [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)
22. [JP2] Jakšić, V., Pillet, C.-A.: On a model for quantum friction III. Ergodic properties of the spin-boson system. Commun. Math. Phys. 178, 627 (1996)
23. [JP3] Jakšić, V., Pillet, C.-A.: On entropy production in quantum statistical mechanics. Commun. Math. Phys. 217, 285 (2001)
24. [JP4] Jakšić, V., Pillet, C.-A.: In preparation
25. [LS] Lebowitz, J., Spohn, S.: Irreversible thermodynamics for quantum systems weakly coupled to thermal reservoirs. Adv. Chem. Phys. 38, 109, New-York: John Wiley and Sons, 1978
26. [O1] Ojima, I.: Entropy production and non-equilibrium stationarity in quantum dynamical systems: physical meaning of van Hove limit. J. Stat. Phys. 56, 203 (1989)
27. [O2] Ojima, I.: Entropy production and non-equilibrium stationarity in quantum dynamical systems. In: Proceedings of international workshop on quantum aspects of optical communications. Lecture Notes in Physics 378, 164. Berlin: Springer-Verlag, 1991
28. [OHI] Ojima, I., Hasegawa, H., Ichiyanagi, M.: Entropy production and its positivity in nonlinear response theory of quantum dynamical systems, J. Stat. Phys. 50, 633 (1988)
29. [OP] Ohya, M., Petz, D.: Quantum Entropy and its Use. Berlin: Springer-Verlag, 1993
30. [M] Merkli, M.: Positive commutators in non-equilibrium quantum statistical mechanics. Commun. Math. Phys. 223, 327 (2001)
31. [Si] Simon, B.: Functional Integration and Quantum Physics. New York: Academic Press, 1979
32. [Ru1] Ruelle, D.: Natural nonequilibrium states in quantum statistical mechanics. J. Stat. Phys, 98, 57 (2000)
33. [Ru2] Ruelle, D.: Entropy production in quantum spin systems. Preprint
34. [Rud] Rudin, W.: Real and Complex Analysis. New York: McGraw Hill, Inc, 1974
35. [Sp1] Spohn, H.: Entropy production for quantum dynamical semigroups. J. Math, Phys. 19, 227 (1978)
36. [Sp2] Spohn, H.: An algebraic condition for the approach to equilibrium of an open N-level system. Lett. Math. Phys. 2, 33 (1977)