From resonances to master equations

 Access to full text

 Full (PDF)

1. [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. Zbl0273.46054MR342080
2. [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). Zbl0392.46043MR675642
3. [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. MR152295
4. [AC] J. Aguilar, and J.M. Combes, A class of analytic perturbations for one-body Schrödinger Hamiltonians. Commun. Math. Phys., 22, 1971, p. 269. Zbl0219.47011MR345551
5. [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. Zbl0219.47005MR345552
6. [BL] F. Bloch, Phys. Rev., 70, 1946, p. 460. 
7. [BLW] F. Bloch and R.K. Wangsness, Phys. Rev., Vol. 89 (1953), p. 728. Zbl0051.22302
8. [BR1] O. Bratteli and D. Robinson, Operator Algebras and Quantum Statistical Mechanics I. Springer-Verlag, New York, 1979. Zbl0421.46048MR611508
9. [BR2] O. Bratteli and D. Robinson, Operator Algebras and Quantum Statistical Mechanics II. Springer-Verlag, New York, 1981. Zbl0463.46052MR611508
10. [D1] E.B. Davies, Markovian master equations. Commun. Math. Phys., Vol. 39, 1974, p. 91. Zbl0294.60080MR359633
11. [D2] E.B. Davies, Markovian master equations. II. Math. Ann., Vol. 219 (1976), p. 147. Zbl0323.60061MR395638
12. [D3] E.B. Davies, Quantum Theory of Open Systems. Academic Press, London, 1976. Zbl0388.46044MR489429
13. [FNV] M. Fannes, B. Nachtergaele and A. Verbeure, The equilibrium states of the spin-boson model. Commun. Math. Phys., Vol. 114, 1988, p. 537. Zbl0653.46064MR929128
14. [H] R. Haag, Local Quantum Physics, Springer-Verlag, Berlin, 1993. Zbl0843.46052MR1182152
15. [HA] F. Haake, Statistical treatment of open systems by generalized master equations. Springer tracts in modern physics, Vol. 66. 
16. [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. Zbl0852.47038MR1376434
17. [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. Zbl0864.47049MR1395208
18. [JP3] V Jakvšić and C.-A. Pillet, On a model for quantum friction IV. Matter and radiation at positive temperature. In preparation. 
19. [KTH] R. Kubo, M. Toda and N. Hashitsume, Statistical Physics II. Nonequilibrium Statistical Mechanics. Springer-Verlag, Berlin, 1985. Zbl0996.60501MR799025
20. [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. 
21. [M] E.W. Montrol, Nonequilibrium Statistical Mechanics. Lectures in Theor. Phys., Vol. 3, p. 221. MR127891
22. [N] S. Nakajima, On quantum theory of transport phenomena. Prog. Theor. Phys., Vol. 20, p. 948. Zbl0084.21505MR102943
23. [P1] W. Pauli, Festschrift zum 60. Gerburtstage A. Sommerfeld, S.30. Leipzig, Hirzel, 1928. 
24. [P2] W. Pauli, Pauli Lectures on Physics: Volume 4.Statistical Mechanics Edited by C.P. Enz. Cambridge, The MIT Press1973. 
25. [PR] I. Prigogine and P. Resibois, On the kinetics of the approach to equilibrium. Physica, Vol. 27, p. 629. Zbl0082.19306MR129869
26. [PU] J.V. Pulé, The Bloch Equations. Commun. Math. Phys., Vol. 38, 1974, p. 241. MR359650
27. [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. 
28. [RO2] D.W. Robinson, Return to equilibrium. Commun. Math. Phys., Vol. 31, 1973, p. 171. Zbl0257.46091MR332078
29. [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. 
30. [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. Zbl0252.47009MR353896
31. [VH1] L. van Hove, Quantum-mechanical perturbations giving rise to a statistical transport equation. Physica, Vol. 21, p. 517. Zbl0065.19505MR71346
32. [VH2] L. van Hove, The approach to equilibrium in quantum statistics. Physica, Vol. 23, p. 441. Zbl0079.19405MR89576
33. [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. 
34. [Z1] R. Zwanzig, Statistical mechanics of irreversibility. Lectures in Theor. Phys, Vol. 3, p. 106. MR127892
35. [Z2] R. Zwanzig, On the identity of three generalized master equations. Physica, Vol. 30, p. 1109. MR183452