Level shift operators for open quantum systems

Journal of Mathematical Analysis and Applications

Volumn 327, Issue 1, 2007, Pages 376-399

  Merkli, Marco ^a,b  

^a MCGILL UNIVERSITY   (Canada)

^b UNIVERSITÉ DE MONTRÉAL   (Canada)

Author keywords

Complex deformation; Ergodic theory; Fermi Golden Rule; KMS states; Open quantum systems; Quantum resonances; Thermal quantum field; Tomita Takesaki theory; von Neumann algebra

Indexed keywords

EID: 33750828099     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2006.04.030     Document Type: Article

References (34)

1. Abou-Salem W.K. On the quasi-static evolution of non-equilibrium steady states. preprint. mp-arc/05-341 J. Statist. Phys., in press
2. Abou-Salem W.K., and Fröhlich J. Adiabatic theorems and reversible isothermal processes. Lett. Math. Phys. 72 2 (2005) 153-163
3. Abou-Salem W.K., and Fröhlich J. Cyclic thermodynamic processes and entropy production. preprint. mp-arc/05-436
4. Araki H. Relative Hamiltonian for faithful normal states of a von Neumann algebra. Publ. Res. Inst. Math. Sci. 9 (1973/1974) 165-209
5. Araki H., and Woods E. Representations of the canonical commutation relations describing a non-relativistic infinite free Bose gas. J. Math. Phys. 4 (1963) 637-662
6. Araki H., and Wyss W. Representations of canonical anticommutation relations. Helv. Phys. Acta 37 (1964) 136-159
7. Bruneau L., and Dereziński J. Bogoliubov Hamiltonians and one-parameter groups of Bogoliubov transformations. preprint. mp-arc/05-398
8. Bisognano J.J., and Wichmann E.H. On the duality condition for a Hermitian scalar field. J. Math. Phys. 16 4 (1975) 985-1007
9. Bach V., Fröhlich J., and Sigal I.M. Quantum electrodynamics of confined nonrelativistic particles. Adv. Math. 137 2 (1998) 299-395
10. Bach V., Fröhlich J., and Sigal I.M. Return to equilibrium. J. Math. Phys. 41 6 (2000) 3985-4060
11. Bratteli O., and Robinson D.W. Operator Algebras and Quantum Statistical Mechanics, vols. I, II. Texts Monogr. Phys. (1987), Springer-Verlag
12. DeBièvre S., and Merkli M. The Unruh effect revisited. preprint. math-ph/0604023
13. Dereziński J., and Früboes R. Level shift operator and second order perturbation theory. J. Math. Phys. 46 3 (2005) 033512, 18 pp
14. Dereziński J., and Früboes R. Fermi Golden Rule and open quantum systems. mp-arc/05-142 Springer Lecture Notes in Math., vol. 1880, in press
15. Dereziński J., and Jakšić V. Return to equilibrium for Pauli-Fierz systems. Ann. Henri Poincaré 4 4 (2003) 739-793
16. Dereziński J., and Jakšić V. On the nature of Fermi Golden Rule for open quantum systems. J. Statist. Phys. 116 1-4 (2004) 411-423
17. *-dynamics, Liouvilleans and KMS-states. Rev. Math. Phys. 15 5 (2003) 447-489
18. Fröhlich J., and Merkli M. Thermal ionization. Math. Phys. Anal. Geom. 7 3 (2004) 239-287
19. Fröhlich J., and Merkli M. Another return of "return to equilibrium,". Comm. Math. Phys. 251 2 (2004) 235-262
20. Fröhlich J., Merkli M., and Sigal I.M. Ionization of atoms in a thermal field. J. Statist. Phys. 116 1-4 (2004) 311-359
21. Jakšić V., and Pillet C.-A. On a model for quantum friction. II. Fermi's Golden Rule and dynamics at positive temperature. Comm. Math. Phys. 176 3 (1996) 619-644
22. Jakšić V., and Pillet C.-A. On a model for quantum friction. III. Ergodic properties of the spin-boson system. Comm. Math. Phys. 178 (1996) 627-651
23. Jakšić V., and Pillet C.-A. Mathematical theory of non-equilibrium quantum statistical mechanics. J. Statist. Phys. 108 5-6 (2002) 787-829
24. Jakšić V., and Pillet C.-A. Non-equilibrium steady states of finite quantum systems coupled to thermal reservoirs. Comm. Math. Phys. 226 1 (2002) 131-162
25. Marder L. An Introduction to Relativity. Mathematical Topics (1968), Longmans, Green, London
26. Martin Ph.A., and Rothen F. Many-Body Problems and Quantum Field Theory. Springer Texts Monogr. Phys. (2002), Springer-Verlag
27. Merkli M. Positive commutators in non-equilibrium quantum statistical mechanics. Comm. Math. Phys. 223 (2001) 327-362
28. M. Merkli, The ideal quantum gas, in: Lecture Notes for the Summerschool on Open Quantum Systems, Institut Fourier, Grenoble, 2003; Springer Lecture Notes in Math., vol. 1880, in press
29. Merkli M., Mück M., and Sigal I.M. Instability of equilibrium states for coupled heat reservoirs at different temperatures. preprint. math-ph/0508005
30. Merkli M., Mück M., and Sigal I.M. Theory of non-equilibrium stationary states as theory of resonances. Existence and properties of NESS. preprint. math-ph/0603006
31. M. Mück, Thermal Relaxation for Particle Systems in Interaction with Several Bosonic Heat Reservoirs, Books on Demand GmbH, Norderstedt, 2004, ISBN 3-8334-1866-4
32. Reed M., and Simon B. Methods of modern mathematical physics, vol. II, Fourier Analysis, Self-Adjointness (1975), Academic Press
33. Sewell G.L. Quantum fields on manifolds: PCT and gravitationally induced thermal states. Ann. of Phys. 141 (1982) 201-224
34. Unruh W.G., and Wald R.M. What happens when an accelerating observer detects a Rindler particle. Phys. Rev. D 29 6 (1984) 1047-1056