On a model for quantum friction. I. Fermi's golden rule and dynamics at zero temperature

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1. [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. Zbl0473.46050MR640665
2. [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. Zbl0473.46051MR640665
3. [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. Zbl0667.46049MR997857
4. [4] H. Cycon, R. Froese, W. Kirsch and B. Simon, Schrödinger Operators, Springer-Verlag, Berlin-Heidelberg, 1987. Zbl0619.47005
5. [5] E.B. Davies, Markovian master equations, Commun. Math. Phys, Vol. 39, 1974, p. 91. Zbl0294.60080MR359633
6. [6] E.B. Davies, Markovian master equations. II. Math. Ann., Vol. 219, 1976, p. 147. Zbl0323.60061MR395638
7. [7] E.B. Davies, Quantum Theory of Open Systems. Academic Press, London, 1976. Zbl0388.46044MR489429
8. [8] E.B. Ford, M. Kac and P. Mazur, Statistical Mechanics of Assemblies of Coupled Oscillators. J. Math. Phys., Vol. 6, 1965, p. 504. Zbl0127.21605MR180277
9. [9] V. Jakšić and C. Pillet, On Model for Quantum Friction II. Fermi's golden rule at positive temperature. Preprint. Zbl0852.47038
10. [10] V. Jakšić, C. Pillet and I.M. Sigal, Return to equilibrium in classical mechanics. In preparation. 
11. [11] T. Okamoto and K. Yajima, Complex Scaling Technique in Nonrelativistic Massive QED. Ann. Inst. Henri Poincaré, Vol. 42, 1985, p 311. Zbl0594.58057MR797278
12. [12] L.S. Ornestein and G.E. Uhlenbeck, On the theory of Brownian motion. Phys. Rev., Vol. 36, 1930, p. 823. JFM56.1277.03
13. [13] M. Reed and B. Simon, Methods of Modern Mathematical Physics, II. Fourier Analysis, Self-Adjointness. Academic Press, London, 1975. Zbl0308.47002MR493420
14. [14] M. Reed and B. Simon, Methods of Modern Mathematical Physics, IV. Analysis of Operators. Academic Press, London, 1978. Zbl0401.47001MR493421
15. [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. Zbl0252.47009MR353896
16. [16] H. Spohn and R. Dümcke, Quantum Tunneling with Dissipation and the Ising Model over R. J. Stat. Phys., Vol. 41, 1985, p. 398. MR814839
17. [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. Zbl0657.60085MR973532

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