Spectral properties of the spin-boson hamiltonian
Annales de l'I.H.P. Physique théorique, Volume 62 (1995) no. 3, p. 289-323
@article{AIHPA_1995__62_3_289_0,
     author = {H\"ubner, Matthias and Spohn, Herbert},
     title = {Spectral properties of the spin-boson hamiltonian},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     publisher = {Gauthier-Villars},
     volume = {62},
     number = {3},
     year = {1995},
     pages = {289-323},
     zbl = {0827.47053},
     mrnumber = {1335060},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1995__62_3_289_0}
}
Hübner, Matthias; Spohn, Herbert. Spectral properties of the spin-boson hamiltonian. Annales de l'I.H.P. Physique théorique, Volume 62 (1995) no. 3, pp. 289-323. http://www.numdam.org/item/AIHPA_1995__62_3_289_0/

[1] A.J. Leggett, S. Chakravarty, A.T. Dorsey, M.P.A. Fisher, A. Garg and W. Zwerger, Dynamics of the Dissipative Two-State System, Rev. Mod. Phys., Vol. 59, 1987, pp. 1-81.

[2] H. Spohn, Ground States(s) of the Spin-Boson Hamiltonian, Comm. Math. Phys., Vol. 123, 1989, pp. 277-304. | MR 1002040 | Zbl 0667.60108

[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. | MR 929128 | Zbl 0653.46064

[4] M. Hübner and H. Spohn, Radiative Decay: Nonperturbative Approaches, Rev. Math. Phys., 1995. | MR 1326139 | Zbl 0843.35068

[5] M. Hübner and H. Spohn, Atom Interacting with Photons: an N-Body Schrödinger Problem (in preparation).

[6] M. Reed and B. Simon, Methods of Modern Mathematical Physics I, Academic Press, New York, 1973. | MR 751959 | Zbl 0242.46001

[7] P.R. Halmos, A Hilbert Space Problem Book, Springer-Verlag, New York, 1982. | MR 675952 | Zbl 0496.47001

[8] A. Arai, On a Model of a Harmonic Oscillator Coupled to a Quantized, Massless Scalar Field, J. Math. Phys., Vol. 22, 1981, pp. 2539-2548 and 2549-2552. | MR 640665 | Zbl 0473.46050

[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. | MR 997857 | Zbl 0667.46049

[10] H.L. Cycon, R.G. Froese, W. Kirsch and B. Simon, Schrödinger Operators, Springer-Verlag, Berlin, 1987. | Zbl 0619.47005

[11] E. Mourre, Absence of Singular Continuous Spectrum for Certain Self-Adjoint Operators, Comm. Math. Phys., Vol. 78, 1981, pp. 391-408. | MR 603501 | Zbl 0489.47010

[12] E. Mourre, Opérateurs conjugués et propriétés de propagation, Comm. Math. Phys., Vol. 91, 1983, pp. 279-300. | MR 723552 | Zbl 0543.47041

[13] E.B. Davies, One-Parameter Semigroups, Academic Press, London, 1980. | MR 591851 | Zbl 0457.47030

[14] K.O. Friedrichs, Perturbations of Spectra in Hilbert Space, AMS, Providence, 1965. | MR 182883 | Zbl 0142.11001

[15] S. Schweber, An Introduction to Relativistic Quantum Field Theory, Row, Petersen and Co., Evanston, 1961. | MR 127796

[16] R. Weder, On the Lee Model with Dilatation Analytic Cutoff Function, J. Math. Phys., Vol. 15, 1975, pp. 20-24. | MR 342089

[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] A. Amann, Ground States of a Spin-Boson Model, Ann. Phys., Vol. 208, 1991, pp. 414-448. | MR 1110433 | Zbl 0875.46010