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The low density limit in finite temperature case

Published online by Cambridge University Press:  22 January 2016

L. Accardi  and
Y. G. Lu
L. Accardi
Affiliation:
Centro Matematico V. Volterra, Dipartimento di Matematica Universita’ di Roma II, Italia
Y. G. Lu
Affiliation:
Centro Matematico V. Volterra, Dipartimento di Matematica Universita’ di Roma II, Italia
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The low density limit in the Boson Fock case has been investigated in [1] where also the physical meaning and their motivations have been explained (cf. also [0]). From these papers one knows how the number processes can be obtained from a quantum Hamiltonian model via a certain limit procedure.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 126 , June 1992 , pp. 25 - 87
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1992

References

[0] Accardi, L., Lu, Y. G., Frigerio, A. and Alicki, R., An invitation to the weak coupling limit and the low density limit, to appear in: Quantum probability and related topics VI, World Scientific, 3 – 31.Google Scholar
[1] Accardi, L., Lu, Y. G., The number process as low density limit of Hamiltonian models, Commun. Math. Phys., 637 (1991), 1–31.Google Scholar
[2] Accardi, L., Frigerio, A., Lu, Y. G., The weak couplihg limit as a functional central limit theorem, Commun. Math. Phys, 131 (1990), 537–570.Google Scholar
[3] Accardi, L., Lu, Y. G., On the low density limit of Boson Models. Lect. Notes in Math, 1442(1988), 17–53.Google Scholar
[4] Accardi, L., Lu, Y. G., The weak coupling limit for nonlinear interactions, Stoch. Proc. Phys. Geom., World Scientific, 1988, 1–26.Google Scholar
[5] Dümcke, R., The low density limit for n-level systems, Lect. Notes in Math, 1136 (1985).Google Scholar
[6] Dümcke, R., The low density limit fot an N-level system interacting with a free Bose or fermi gas, Commun. Math. Phys., 97 (1985), 331–359.CrossRefGoogle Scholar
[7] Frogerio, A., Maassen, H., Quantum Poisson processes and dilations of dynamical semigroups, Prob. Th. Rel. Fields., 83 (1989), 489–508.Google Scholar
[8] Grad, H., Principles of the knietic theory of Gases, Handbuch der Physik, vol. 12, Springer (1958).Google Scholar
[9] Hudson, R. L., Pathasarathy, K. R., Quantum Ito’s formula and stochastic evolution, Commun. Math. Phys., 93 (1984), 301–323.CrossRefGoogle Scholar
[10] Palmer, P. F.; Thesis, Oxford University.Google Scholar
[11] Patz, D.; An invitation to the C*-algebra of the canonical commutation relation, Leuven Notes in Math, and Theor. Phys., eds. Fannes, M. Verbeure, A., Leuven Univ. Press 1990.Google Scholar