Return to Equilibrium for Pauli-Fierz Systems

Annales Henri Poincare

Volumn 4, Issue 4, 2003, Pages 739-793

  Dereziński, Jan ^a   Jakšić, Vojkan ^b  

^a UNIVERSITY OF WARSAW   (Poland)

^b MCGILL UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0345491555     PISSN: 14240637     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00023-003-0146-4     Document Type: Article

References (32)

1. [AH] A. Arai, M. Hirokawa, On the existence and uniqueness of ground states of the spin-boson Hamiltonian, J. Func. Anal. 151, 455 (1997).
2. [Ar] H. Araki, Relative Hamiltonian for faithful normal states of a von Neumann algebra, Pub. R.I.M.S. Kyoto Univ. 9, 165 (1973).
3. [AW] H. Araki, E.J. Woods, Representations of the canonical commutation relations describing a nonrelativistic infinite free Bose gas, J. Math. Phys. 4, 637 (1963).
4. [BFS1] V. Bach, J. Fröhlich, I. Sigal, Quantum electrodynamics of confined non-relativistic particles, Adv. Math. 137, 299 (1998).
5. [BFS2] V. Bach, J. Fröhlich, I. Sigal, Return to equilibrium, Journ. Math. Phys. 41, 3985 (2000).
6. [BFSS] V. Bach, J. Fröhlich, I. Sigal, A. Soffer, Positive commutators and the spectrum of Pauli-Fierz Hamiltonian of atoms and molecules, Comm. Math. Phys. 207, 557 (1999).
7. [BR1] O. Brattelli, D.W. Robinson Operator Algebras and Quantum Statistical Mechanics, Volume 1, Springer-Verlag, Berlin, second edition 1987.
8. [BR2] O. Brattelli, D.W. Robinson Operator Algebras and Quantum Statistical Mechanics, Volume 2, Springer-Verlag, Berlin, second edition 1996.
9. [Da] E.B. Davies, Markovian master equations, Comm. Math. Phys. 39, 91 (1974).
10. [DG] J. Dereziński, C. Gérard, Asymptotic completeness in quantum field theory. Massive Pauli-Fierz Hamiltonians, Rev. Math. Phys. 11, 383 (1999).
11. [DJ1] J. Dereziński, V. Jakšić, Spectral theory of Pauli-Fierz operators, Journ. Func. Anal. 180 , 241 (2001).
12. [DJ2] J. Dereziński, V. Jakšić, in preparation.
13. [DJP] J. Dereziński, V. Jakšić, C.-A. Pillet, Perturbation theory of W*-dynamics, Liouvilleans and KMS-states, to appear in Rev. Math. Phys.
14. [FNV] M. Fannes, B. Nachtergale, A. Verbeure, The equilibrium states of the spin-boson model, Comm. Math. Phys. 114, 537 (1988).
15. [Fr] A. Frigerio, Stationary states of quantum dynamical semigroups, Comm. Math. Phys. 63, 269 (1978).
16. [FGS] J. Fröhlich, M. Griesemer, B. Schiein, Asymptotic completeness for Rayleigh scattering, Ann. Inst. Henri Poincaré 3, 107 (2002).
17. [Ge] C. Gérard, On the existence of ground states for massless Pauli-Fierz Hamiltonians, Ann. Inst. Henri Poincaré 1, 443 (2000).
18. [HS1] M. Hübner, S. Spohn, Radiative decay: non-perturbative approaches, Rev. Math. Phys. 8, 549 (1996).
19. [HS2] M. Hübner, S. Spohn, Spectral properties of the spin-boson Hamiltonian, Ann. Inst. Henri Poincaré 62, 289 (1995).
20. [Ja] A.Z. Jadczyk, On some groups of automorphisms of von Neumann algebras with cyclic and separating vectors, Comm. Math. Phys. 13, 142 (1969).
21. [JP1] V. Jakšić, C.-A. Pillet, On a model for quantum friction II: Fermi's golden rule and dynamics at positive temperature, Comm. Math. Phys. 176, 619 (1996).
22. V. Jakšić, C.-A. Pillet, On a model for quantum friction III: Ergodic properties of the spin-boson system, Comm. Math. Phys. 178, 627 (1996).
23. [JP3] V. Jakšić, C.-A. Pillet, Non-equilibrium steady states for finite quantum systems coupled to thermal reservoirs, Comm. Math. Phys. 226, 131 (2002).
24. [M] M. Merkli, Positive commutators in non-equilibrium quantum statistical mechanics, Comm. Math. Phys. 223, 327 (2001).
25. [PF] W. Pauli, M. Fierz, Nuovo Cimento 15, 167 (1938).
26. [OY] T. Okamoto, K. Yajima, Complex scaling technique in non-relativistic qed, Ann. Inst. Henri Poincaré 42, 391 (1981).
27. [Ru] D. Ruelle, Natural nonequilibrium states in quantum statistical mechanics, J. Stat. Phys. 98, 57 (2000).
28. [Sk] E. Skibsted, Spectral analysis of N-body systems coupled to a bosonic system, Rev. Math. Phys. 10, 989 (1998).
29. [Sp1] H. Spohn, An algebraic condition for the approach to equilibrium of an open TV-level system, Lett. Math. Phys. 2, 33 (1977).
30. [Sp2] H. Spohn, Ground states of the spin-boson Hamiltonian, Comm. Math. Phys. 123, 277 (1989).
31. [Sp3] H. Spohn, Ground state of a quantum particle coupled to a scalar Bose field, Lett. Math. Phys. 44, 9 (1998).
32. [St] S. Stratila, Modular Theory in Operator Algebras, Abacus Press, Turnbridge Wells 1981.