Thermal ionization

Mathematical Physics Analysis and Geometry

Volumn 7, Issue 3, 2004, Pages 239-287

  Fröhlich, Jürg ^a   Merkli, Marco ^a,b  

^a ETH ZURICH   (Switzerland)

^b MCGILL UNIVERSITY   (Canada)

Author keywords

Black body radiation; CCR algebra; Fermi Golden Rule; Liouville operator; Mourr estimate; Open quantum system; Positive commutators; Standard form of von Neumann algebras; Virial theorem

Indexed keywords

EID: 3242730556     PISSN: 13850172     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:MPAG.0000034613.13746.8a     Document Type: Article

References (17)

1. 0-Groups, Commutator Methods and Spectral Theory of N-body Hamiltonians, Birkhäuser, Basel, 1996.
2. [Ara] Araki, H.: Some properties of modular conjugation operator of von Neumann algebras and a noncommutative Radon-Nicodym theorem with a chain rule, Pacific J. Math. 50(2) (1974), 309-354.
3. [AW] Araki, H. and Woods, E.: Representations of the canonical commutation relations describing a nonrelativistic infinite free bose gas, J. Math. Phys. 4 (1963), 637-662.
4. [BFS] Bach, V., Fröhlich, J. and Sigal, I. M.: Quantum electrodynamics of confined nonrelativistic particles, Adv. Math. 137(2) (1995), 299-395.
5. [BFSS] Bach, V., Fröhlich, J., Sigal, I. M. and Soffer, A.: Positive commutators and the spectrum of Pauli-Fierz Hamiltonians of atoms and molecules, Comm. Math. Phys. 207(3) (1999), 557-587.
6. [BRI, II] Bratteli, O. and Robinson, D.: Operator Algebras and Quantum Statistical Mechanics I, II, 2nd edn, Texts Monogr. Phys., Springer, Berlin, 1987.
7. [Con] Connes, A.: Caractérisation des algèbres de von Neumann comme espaces vectroriels ordonnés, Ann. Inst. Fourier (Grenoble) 24 (1974), 121-155.
8. [DJ] Dereziński, J. and Jakšić, V.: Spectral theory of Pauli-Fierz operators, J. Funct. Anal. 180 (2001), 243-327.
9. [DJP] Dereziński, J., Jakšić, V. and Pillet, C.-A.: Perturbation theory for W*-dynamics, Liouvilleans and KMS-states, Preprint.
10. [Frö] Fröhlich, J.: Application of commutator theorems to the integration of representations of Lie algebras and commutation relations, Comm. Math. Phys. 54 (1977), 135-150.
11. [FGS] Fröhlich, J., Griesemer, M. and Schlein, B.: Asymptotic completeness for Rayleigh scattering, Ann. Inst. H. Poincaré 3 (2002), 107-170.
12. [GG] Georgescu, V. and Gérard, C.: On the virial theorem in quantum mechanics, Comm. Math. Phys. 208 (1999), 275-281.
13. [Haa] Haagerup, U.: The standard form of von Neumann algebras, Math. Scand. 37 (1975), 271-283.
14. [JP] Jakšić, V. and Pillet, C.-A.: On a model for quantum friction III. Ergodic properties of the spin-boson system, Comm. Math. Phys. 178 (1996), 627-651.
15. [Mer] Merkli, M.: Positive commutators in nonequilibrium quantum statistical mechanics, Comm. Math. Phys. 223 (2001), 327-362.
16. [Mou] Mourre, E.: Absence of singular continuous spectrum for certain self-adjoint operators, Comm. Math. Phys. 91 (1981), 391-408.
17. [Ski] Skibsted, E.: Spectral analysis of N-body systems coupled to a bosonic field, Rev. Math. Phys. 10(7) (1998), 989-1026.