On a model for quantum friction. I. Fermi's golden rule and dynamics at zero temperature
Annales de l'I.H.P. Physique théorique, Volume 62 (1995) no. 1, pp. 47-68.
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     author = {Jak\v{s}i\'c, V. and Pillet, C. A.},
     title = {On a model for quantum friction. {I.} {Fermi's} golden rule and dynamics at zero temperature},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
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     url = {http://archive.numdam.org/item/AIHPA_1995__62_1_47_0/}
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Jakšić, V.; Pillet, C. A. On a model for quantum friction. I. Fermi's golden rule and dynamics at zero temperature. Annales de l'I.H.P. Physique théorique, Volume 62 (1995) no. 1, pp. 47-68. http://archive.numdam.org/item/AIHPA_1995__62_1_47_0/

[1] A. Arai, On a model of a harmonic oscillator coupled to a quantized, massless, scalar field, I. J. Math. Phys., Vol. 22, 1981, p. 2539. | MR | Zbl

[2] A. Arai, On a model of a harmonic oscillator coupled to a quantized, massless, scalar field, II. J. Math. Phys., Vol. 22, 1981, p. 2549. | MR | Zbl

[3] A. Arai, Spectral Analysis of a Quantum Harmonic Oscillator Coupled to Infinitely Many Scalar Bosons, J. Math. Anal. Appl., Vol. 140, 1989, p. 270. | MR | Zbl

[4] H. Cycon, R. Froese, W. Kirsch and B. Simon, Schrödinger Operators, Springer-Verlag, Berlin-Heidelberg, 1987. | Zbl

[5] E.B. Davies, Markovian master equations, Commun. Math. Phys, Vol. 39, 1974, p. 91. | MR | Zbl

[6] E.B. Davies, Markovian master equations. II. Math. Ann., Vol. 219, 1976, p. 147. | MR | Zbl

[7] E.B. Davies, Quantum Theory of Open Systems. Academic Press, London, 1976. | MR | Zbl

[8] E.B. Ford, M. Kac and P. Mazur, Statistical Mechanics of Assemblies of Coupled Oscillators. J. Math. Phys., Vol. 6, 1965, p. 504. | MR | Zbl

[9] V. Jakšić and C. Pillet, On Model for Quantum Friction II. Fermi's golden rule at positive temperature. Preprint.

[10] V. Jakšić, C. Pillet and I.M. Sigal, Return to equilibrium in classical mechanics. In preparation.

[11] T. Okamoto and K. Yajima, Complex Scaling Technique in Nonrelativistic Massive QED. Ann. Inst. Henri Poincaré, Vol. 42, 1985, p 311. | Numdam | MR | Zbl

[12] L.S. Ornestein and G.E. Uhlenbeck, On the theory of Brownian motion. Phys. Rev., Vol. 36, 1930, p. 823. | JFM

[13] M. Reed and B. Simon, Methods of Modern Mathematical Physics, II. Fourier Analysis, Self-Adjointness. Academic Press, London, 1975. | MR | Zbl

[14] M. Reed and B. Simon, Methods of Modern Mathematical Physics, IV. Analysis of Operators. Academic Press, London, 1978. | MR | Zbl

[15] B. Simon, Resonances in N-body quantum systems with dilation analytic potentials and the foundations of time-dependent perturbation theory. Ann. Math., Vol. 97, 973, p. 247. | MR | Zbl

[16] H. Spohn and R. Dümcke, Quantum Tunneling with Dissipation and the Ising Model over R. J. Stat. Phys., Vol. 41, 1985, p. 398. | MR

[17] P. Smedt, D. Dürr, J. Lebowitz and C. Liverani, Quantum System in Contact with a Thermal Enviroment: Rigorous Treatment of a Simple Model. Commun. Math. Phys., Vol. 120, 1988, p. 195. | MR | Zbl