On the existence and uniqueness of ground states of a generalized spin-boson model

Journal of Functional Analysis

Volumn 151, Issue 2, 1997, Pages 455-503

  Arai, Asao ^a   Hirokawa, Masao ^b  

^a HOKKAIDO UNIVERSITY   (Japan)

^b TOKYO GAKUGEI UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031574581     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1997.3140     Document Type: Article

References (26)

1. Amann A. Ground states of a spin-boson model. Ann. Phys. 208:1991;414-448.
2. Arai A. On a model of a harmonic oscillator coupled to a quantized, massless, scalar field, I. J. Math. Phys. 22:1981;2539-2548.
3. Arai A. Rigorous theory of spectra and radiation for a model in quantum electrodynamics. J. Math. Phys. 24:1981;1896-1910.
4. Arai A. Spectral analysis of a quantum harmonic oscillator coupled to infinitely many scalar bosons. J. Math. Anal. Appl. 140:1989;270-288.
5. Arai A. Perturbation of embedded eigenvalues: A general class of exactly soluble models in Fock spaces. Hokkaido Math. J. 19:1990;1-34.
6. Arai A. An asymptotic analysis and its application to the non-relativistic limit of the Pauli-Fierz and a spin-boson model. J. Math. Phys. 31:1990;2653-2663.
7. Arai A., Hirokawa M. Hokkaido University Preprint Series in Mathematics. 309:1995.
8. A. Arai, M. Hirokawa, 1996, On the spin-boson model, Proceedings of the Symposium Quantum Stochastic Analysis and Related Fields Held at the RIMS, Kyoto University, November 27-29, 1995, 957, 16, 35, RIMS Kokyuroku.
9. Bach V., Fröhlich J., Sigal I. Mathematical theory of nonrelativistic matter and radiation. Lett. Math. Phys. 34:1995;183-201.
10. V. Bach, J. Fröhlich, I. Sigal, 1996, Quantum electrodynamics of confined nonrelativistic particles.
11. Davies E. B. Symmetry breaking for molecular open system. Ann. Inst. H. Poincaré A. 35:1981;149-171.
12. Fannes M., Nachtergaele B., Verbeure A. The equilibrium state of the spin-boson model. Comm. Math. Phys. 114:1988;537-548.
13. Fröhlich J. Existence of dressed one electron states in a class of persistent models. Fortschr. Phys. 22:1973;159-198.
14. Fröhlich J. On the infrared problem in a model of scalar electrons and massless, scalar bosons. Ann. Inst. H. Poincaré A. 19:1973;1-103.
15. Gérard C. Asymptotic completeness for the spin-boson model with a particle number cutoff. Rev. Math. Phys. 8:1996;549-589.
16. 2. Ann. of Math. 91:1970;362-401.
17. Hübner M., Spohn H. Spectral properties of the spin-boson Hamiltonian. Ann. Inst. H. Poincaré 62:1995;289-323.
18. Hübner M., Spohn H. Radiative decay: Nonperturbative approach. Rev. Math. Phys. 7:1995;363-387.
19. Jakšić V., Pillet C. A. On a model for quantum friction. I. Fermi's golden rule and dynamics at zero temperature. Ann. Inst. H. Poincaré 62:1995;47-68.
20. Jakšić V., Pillet C. A. On a model for quantum friction. II. Fermi's golden rule and dynamics at positive temperature. Comm. Math. Phys. 176:1996;619-644.
21. Reed M., Simon B. Methods of Modern Mathematical Physics. 1972;Academic Press, New York.
22. Reed M., Simon B. Methods of Modern Mathematical Physics. 1974;Academic Press, New York.
23. Reed M., Simon B. Methods of Modern Mathematical Physics. 1978;Academic Press, New York.
24. Simon B., Hoegh-Krohn R. Hypercontractive semigroups and two dimensional self-coupled Bose fields. J. Funct. Anal. 9:1972;121-180.
25. Spohn H. Ground state(s) of the spin-boson Hamiltonian. Comm. Math. Phys. 123:1989;277-304.
26. H. Spohn, 1996, Asymptotic completeness for Rayleigh scattering.