An Expression of the Ground State Energy of the Spin-Boson Model

Journal of Functional Analysis

Volumn 162, Issue 1, 1999, Pages 178-218

  Hirokawa, Masao ^a  

^a TOKYO GAKUGEI UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040955608     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1998.3369     Document Type: Article

References (41)

1. Accardi L., Kozyrev S. V., Volovich I. V. Dynamics of dissipative two-level systems in the stochastic approximation. Phys. Rev. A. 56:1997;1-6.
2. Amann A. Ground states of a spin-boson model. Ann. Phys. 208:1991;414-448.
3. Arai A. An asymptotic analysis and its applications to the non-relativistic limit of the Pauli-Fierz and a spin-boson model. J. Math. Phys. 31:1990;2653-2663.
4. Arai A. Perturbation of embedded eigenvalues: A general class of exactly soluble models in Fock spaces. Hokkaido Math. J. 19:1990;1-34.
5. Arai A., Hirokawa M. On the spin-boson model. Proceedings of the symposium Quantum Stochastic Analysis and related Fields. November 27-29, 1995;Kyoto UniversityRIMS.
6. Arai A., Hirokowa M. On the existence and uniqueness of ground states of a generalized spin-boson model. J. Funct. Anal. 151:1997;455-503.
7. Bach V., Fröhlich J., Sigal I. M. Mathematical theory of nonrelativistic matter and radiation. Lett. Math. Phys. 34:1995;183-201.
8. Bach V., Fröhlich J., Sigal I. M. Quantum electrodynamics of confined nonrelativistic particles. Adv. in Math. 137:1998;299-395.
9. f1.
10. Bach V., Fröhlich J., Sigal I. M. Renormalization group analysis of spectral problem in quantum field theory. Adv. in Math. 137:1998;205-298.
11. Bloch C. Sur la détermination de l'état fondamental d'un système de particules. Nucl. Phys. 7:1958;451-458.
12. Davies E. B. Symmetry breaking for molecular open system. Ann. Inst. H. Poincaré A. 35:1981;149-171.
13. Donsker M., Varadhan S. R. S. Asymptotic evaluation certain Markov process expectations for large times IV. Commun. Pure Appl. Math. 36:1983;183-212.
14. Donsker M., Varadhan S. R. S. Asymptotic for the polaron. Commun. Pure Appl. Math. 36:1983;505-528.
15. Ezawa H., Arai A. Quantum Fields Theory and Statistical Mechanics. 1988;Nihon Hyoron Sha, Tokyo.
16. Fannes M., Nachtergaele B., Verbeure A. The equilibrium state of the spin-boson model. Comm. Math. Phys. 114:1988;537-548.
17. Fefferman C., Fröhlich J., Graf G. M. Stability of ultraviolet-cutoff quantum electrodynamics with non-relativistic matter. Comm. Math. Phys. 190:1997;309-330.
18. Gérard C. Asymptotic completeness for the spin-boson model with a particle number cutoff. Rev. Math. Phys. 8:1996;549-589.
19. 2. Ann. of Math. 91:1970;362-401.
20. M. Hirokawa, An inverse problem in quantum field theory and canonical correlation functions: An application of a solvable model called the rotating wave approximation, J. Math. Soc. of Japan.
21. Hübner M., Spohn H. Spectral properties of the spin-boson Hamiltonian. Ann. Inst. H. Poincaré 62:1995;289-323.
22. Hübner M., Spohn H. Radiative decay: Nonperturbative approach. Rev. Math. Phys. 7:1995;363-387.
23. 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.
24. 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.
25. V. Jakšić, C.-A. Pillet, Spectral theory of thermal relaxation in the spin-boson model, IAMP XIIth ICMP 13-19 July 1997.
26. Kireev A. N., Mann A. Tunneling and localization in a two-state system interacting with a phonon bath. Phys. Rev. B. 52:1995;9182-9185.
27. Leggett A. J., Chakravarty S., Dorsey A. T., Fisher M. P. A., Garg A., Zwerger W. Dynamics of the dissipative two-state system. Rev. Mod. Phys. 59:1987;1-85.
28. Lieb E. H., Thomas L. E. Exact ground state energy of the strong-coupling polaron. Comm. Math. Phys. 183:1997;511-519.
29. Reed M., Simon B. Methods of Modern Mathematical Physics. 1972;Academic Press, New York.
30. Reed M., Simon B. Methods of Modern Mathematical Phyics. 1975;Academic Press, New York.
31. Reed M., Simon B. Methods of Modern Mathematical Physics. 1978;Academic Press, New York.
32. Simon B., Hoegh-Krohn R. Hypercontractive semigroups and two dimensional self-adjoint Bose fields. J. Funct. Anal. 9:1972;121-180.
33. Spohn H. Ground state(s) of the spin-boson Hamiltonian. Comm. Math. Phys. 123:1989;277-304.
34. H. Spohn, Asymptotic completeness for Rayleigh scattering, 1996.
35. Spohn H. Ground state of a quantum particle coupled to a scalar Boson field. Lett. Math. Phys. 44:1998;9-16.
36. Tomonaga S. On the effect of the field reactions on the interaction of mesotrones and nuclear particles I. Prog. Theo. Phys. 1:1946;83-101.
37. Tomonaga S. On the effect of the field reactions on the interaction of mesotrones and nuclear particles II. Prog. Theo. Phys. 1:1946;109-124.
38. Tomonaga S. On the effect of the field reactions on the interaction of mesotrones and nuclear particles III. Prog. Theo. Phys. 2:1947;6-24.
39. Tomonaga S. On the effect of the field reactions on the interaction of mesotrones and nuclear particles IV. Prog. Theo. Phys. 2:1947;63-70.
40. Tsuzuki T. Ground state of a spin-boson system, The dynamic compensation theorem and the orthogonality theorem. Prog. Theo. Phys. 82:1989;917-929.
41. Tsuzuki T. Ground stater of a spin-boson system II, Wavefunction and variational study. Prog. Theo. Phys. 87:1992;569-581.