Spectral properties of the spin-boson hamiltonian

Matthias Hübner; Herbert Spohn

Annales de l'I.H.P. Physique théorique (1995)

  • Volume: 62, Issue: 3, page 289-323
  • ISSN: 0246-0211

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Hübner, Matthias, and Spohn, Herbert. "Spectral properties of the spin-boson hamiltonian." Annales de l'I.H.P. Physique théorique 62.3 (1995): 289-323. <http://eudml.org/doc/76677>.

@article{Hübner1995,
author = {Hübner, Matthias, Spohn, Herbert},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Mourre type estimate; complete spectral characterization of the spin- boson Hamiltonian; singular continuous spectrum; ground state energy; Friedrichs model; rotating wave approximation; spin-boson model},
language = {eng},
number = {3},
pages = {289-323},
publisher = {Gauthier-Villars},
title = {Spectral properties of the spin-boson hamiltonian},
url = {http://eudml.org/doc/76677},
volume = {62},
year = {1995},
}

TY - JOUR
AU - Hübner, Matthias
AU - Spohn, Herbert
TI - Spectral properties of the spin-boson hamiltonian
JO - Annales de l'I.H.P. Physique théorique
PY - 1995
PB - Gauthier-Villars
VL - 62
IS - 3
SP - 289
EP - 323
LA - eng
KW - Mourre type estimate; complete spectral characterization of the spin- boson Hamiltonian; singular continuous spectrum; ground state energy; Friedrichs model; rotating wave approximation; spin-boson model
UR - http://eudml.org/doc/76677
ER -

References

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  2. [2] H. Spohn, Ground States(s) of the Spin-Boson Hamiltonian, Comm. Math. Phys., Vol. 123, 1989, pp. 277-304. Zbl0667.60108MR1002040
  3. [3] M. Fannes, B. Nachtergaele and A. Verbeure, The Equilibrium States of the Spin-Boson Model, Comm. Math. Phys., Vol. 114, 1988, pp. 537-548. Zbl0653.46064MR929128
  4. [4] M. Hübner and H. Spohn, Radiative Decay: Nonperturbative Approaches, Rev. Math. Phys., 1995. Zbl0843.35068MR1326139
  5. [5] M. Hübner and H. Spohn, Atom Interacting with Photons: an N-Body Schrödinger Problem (in preparation). 
  6. [6] M. Reed and B. Simon, Methods of Modern Mathematical Physics I, Academic Press, New York, 1973. Zbl0242.46001MR751959
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  9. [9] A. Arai, Spectral Analysis of a Quantum Harmonic Oscillator Coupled to Infinitely Many Scalar Bosons, J. Math. Anal. Appl., Vol. 140, 1989, pp. 270-288. Zbl0667.46049MR997857
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  12. [12] E. Mourre, Opérateurs conjugués et propriétés de propagation, Comm. Math. Phys., Vol. 91, 1983, pp. 279-300. Zbl0543.47041MR723552
  13. [13] E.B. Davies, One-Parameter Semigroups, Academic Press, London, 1980. Zbl0457.47030MR591851
  14. [14] K.O. Friedrichs, Perturbations of Spectra in Hilbert Space, AMS, Providence, 1965. Zbl0142.11001MR182883
  15. [15] S. Schweber, An Introduction to Relativistic Quantum Field Theory, Row, Petersen and Co., Evanston, 1961. Zbl0111.43102MR127796
  16. [16] R. Weder, On the Lee Model with Dilatation Analytic Cutoff Function, J. Math. Phys., Vol. 15, 1975, pp. 20-24. MR342089
  17. [17] V. Enss, Geometric Methods in Spectral and Scattering Theory of Schrödinger Operators. In: Rigorous Atomic and Molecular Physics, pp. 7-69. G. VELO and A. WIGHTMAN Eds., Plenum, New York, 1981. 
  18. [18] A. Amann, Ground States of a Spin-Boson Model, Ann. Phys., Vol. 208, 1991, pp. 414-448. Zbl0875.46010MR1110433

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