From resonances to master equations
Annales de l'I.H.P. Physique théorique, Tome 67 (1997) no. 4, pp. 425-445.
@article{AIHPA_1997__67_4_425_0,
     author = {Jak\v{s}i\'c, Vojkan and Pillet, Claude-Alain},
     title = {From resonances to master equations},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {425--445},
     publisher = {Gauthier-Villars},
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     number = {4},
     year = {1997},
     mrnumber = {1632244},
     zbl = {0910.60084},
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     url = {http://www.numdam.org/item/AIHPA_1997__67_4_425_0/}
}
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Jakšić, Vojkan; Pillet, Claude-Alain. From resonances to master equations. Annales de l'I.H.P. Physique théorique, Tome 67 (1997) no. 4, pp. 425-445. http://www.numdam.org/item/AIHPA_1997__67_4_425_0/

[A1] H. Araki, Relative Hamiltonian for faithful normal states of a von Neumann algebra. Pub. R.I.M.S. Kyoto Univ. Vol. 9, 1973, p. 165. | MR 342080 | Zbl 0273.46054

[A2] H. Araki, Positive cone, Radon-Nikodym theorems, relative Hamiltonian and the Gibbs condition in statistical mechanics. An application of the Tomita-Takesaki theory, in C*-Algebras and Their Applications to Statistical Mechanics and Quantum Field Theory, D. Kastler, ed., Editrice Composition, Bologna (1975). | MR 675642 | Zbl 0392.46043

[AW] H. Araki and E.J. Woods, Representation of the canonical commutation relations describing a non relativistic infinite free Bose gas. J. Math. Phys., Vol. 4, 1963, p. 637. | MR 152295

[AC] J. Aguilar, and J.M. Combes, A class of analytic perturbations for one-body Schrödinger Hamiltonians. Commun. Math. Phys., 22, 1971, p. 269. | MR 345551 | Zbl 0219.47011

[BC] E. Balslev and J.M. Combes, Spectral properties of many-body Schrödinger operators with dilation analytic interactions. Commun. Math. Phys., Vol. 22, 1971, p. 280. | MR 345552 | Zbl 0219.47005

[BL] F. Bloch, Phys. Rev., 70, 1946, p. 460.

[BLW] F. Bloch and R.K. Wangsness, Phys. Rev., Vol. 89 (1953), p. 728. | Zbl 0051.22302

[BR1] O. Bratteli and D. Robinson, Operator Algebras and Quantum Statistical Mechanics I. Springer-Verlag, New York, 1979. | MR 611508 | Zbl 0421.46048

[BR2] O. Bratteli and D. Robinson, Operator Algebras and Quantum Statistical Mechanics II. Springer-Verlag, New York, 1981. | MR 611508 | Zbl 0463.46052

[D1] E.B. Davies, Markovian master equations. Commun. Math. Phys., Vol. 39, 1974, p. 91. | MR 359633 | Zbl 0294.60080

[D2] E.B. Davies, Markovian master equations. II. Math. Ann., Vol. 219 (1976), p. 147. | MR 395638 | Zbl 0323.60061

[D3] E.B. Davies, Quantum Theory of Open Systems. Academic Press, London, 1976. | MR 489429 | Zbl 0388.46044

[FNV] M. Fannes, B. Nachtergaele and A. Verbeure, The equilibrium states of the spin-boson model. Commun. Math. Phys., Vol. 114, 1988, p. 537. | MR 929128 | Zbl 0653.46064

[H] R. Haag, Local Quantum Physics, Springer-Verlag, Berlin, 1993. | MR 1182152

[HA] F. Haake, Statistical treatment of open systems by generalized master equations. Springer tracts in modern physics, Vol. 66.

[JP1] V Jakvšić and C.-A. Pillet, On a model for quantum friction II. Fermi's golden rule and dynamics at positive temperature. Commun. Math. Phys., Vol. 176 (1996), p. 619. | MR 1376434 | Zbl 0852.47038

[JP2] V Jakšić and C.-A. Pillet, On a model for quantum friction III. Ergodic properties of the spin-boson system. Commun. Math. Phys., Vol. 178, 1996, p. 627. | MR 1395208 | Zbl 0864.47049

[JP3] V Jakvšić and C.-A. Pillet, On a model for quantum friction IV. Matter and radiation at positive temperature. In preparation.

[KTH] R. Kubo, M. Toda and N. Hashitsume, Statistical Physics II. Nonequilibrium Statistical Mechanics. Springer-Verlag, Berlin, 1985. | MR 799025

[LCD] A.J. Legget, Chakravarty S., Dorsey A.T., Fisher M.P.A., Garg A. and Zwerger W., Dynamics of the dissipative two-state system. Rev. Mod. Phys., Vol. 59, 1987, p. 1.

[M] E.W. Montrol, Nonequilibrium Statistical Mechanics. Lectures in Theor. Phys., Vol. 3, p. 221. | MR 127891

[N] S. Nakajima, On quantum theory of transport phenomena. Prog. Theor. Phys., Vol. 20, p. 948. | MR 102943 | Zbl 0084.21505

[P1] W. Pauli, Festschrift zum 60. Gerburtstage A. Sommerfeld, S.30. Leipzig, Hirzel, 1928.

[P2] W. Pauli, Pauli Lectures on Physics: Volume 4.Statistical Mechanics Edited by C.P. Enz. Cambridge, The MIT Press 1973.

[PR] I. Prigogine and P. Resibois, On the kinetics of the approach to equilibrium. Physica, Vol. 27, p. 629. | MR 129869

[PU] J.V. Pulé, The Bloch Equations. Commun. Math. Phys., Vol. 38, 1974, p. 241. | MR 359650

[RO1] D.W. Robinson, C*-algebras and quantum statistical mechanics, in C*-Algebras and Their Applications to Statistical Mechanics and Quantum Field Theory, D. Kastler, ed., Editrice Composition, Bologna, 1975.

[RO2] D.W. Robinson, Return to equilibrium. Commun. Math. Phys., Vol. 31, 1973, p. 171. | MR 332078 | Zbl 0257.46091

[SD] H. Spohn and R. Dümcke, The proper form of the generator in the weak coupling limit. Z. Physik B, Vol. 34, 1979, p. 419.

[SI] B. Simon, Resonances in N-body quantum systems with dilation analytic potentials and the foundations of time-dependent perturbation theory. Ann. Math., Vol. 97, 1973, p. 247. | MR 353896 | Zbl 0252.47009

[VH1] L. Van Hove, Quantum-mechanical perturbations giving rise to a statistical transport equation. Physica, Vol. 21, p. 517. | MR 71346 | Zbl 0065.19505

[VH2] L. Van Hove, The approach to equilibrium in quantum statistics. Physica, Vol. 23, p. 441. | MR 89576 | Zbl 0079.19405

[VH3] L. Van Hove, Master equation and approach to equilibrium for quantum systems. In Fundamental problems in statistical mechanics, compiled by E.G.D. Cohen, North-Holland, Amsterdam, 1962.

[Z1] R. Zwanzig, Statistical mechanics of irreversibility. Lectures in Theor. Phys, Vol. 3, p. 106. | MR 127892

[Z2] R. Zwanzig, On the identity of three generalized master equations. Physica, Vol. 30, p. 1109. | MR 183452