Abstract:
In the framework of the theory of the canonical ensemble, a rigorous mathematical
description is given of equilibrium states of quantum systems that satisfy Bose or
Fermi statistics at low densities. Study of the properties of the solutions of the
corresponding Kirkwood–Salsburg equations leads to proof of the existence and
uniqueness of limit partial density matrices of the canonical ensemble as analytic
functions of the density; the equivalence of the canonical and the grand canonical
ensembles in the thermodynamic limit is proved.
Citation:
K. S. Matviichuk, “Mathematical description of the states of bose and fermi systems by the method of partial density matrices of the canonical ensemble”, TMF, 41:3 (1979), 346–367; Theoret. and Math. Phys., 41:3 (1979), 1067–1079
\Bibitem{Mat79}
\by K.~S.~Matviichuk
\paper Mathematical description of the states of bose and fermi systems by the method of partial density matrices of the canonical ensemble
\jour TMF
\yr 1979
\vol 41
\issue 3
\pages 346--367
\mathnet{http://mi.mathnet.ru/tmf3067}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=566306}
\transl
\jour Theoret. and Math. Phys.
\yr 1979
\vol 41
\issue 3
\pages 1067--1079
\crossref{https://doi.org/10.1007/BF01019377}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1979JV61100006}
Linking options:
https://www.mathnet.ru/eng/tmf3067
https://www.mathnet.ru/eng/tmf/v41/i3/p346
This publication is cited in the following 3 articles:
Yu. M. Sukhov, “Linear boson models of time evolution in quantum statistical mechanics”, Math. USSR-Izv., 24:1 (1985), 151–182
K. S. Matviichuk, “Conditions of existence and stability of a solution of singular Kirkwood–Salsburg equations. Part III”, Theoret. and Math. Phys., 51:1 (1982), 372–381
K. S. Matviichuk, “Conditions of existence and stability of a solution of singular Kirkwood–Salsburg equations. Parts I and II”, Theoret. and Math. Phys., 49:1 (1981), 887–896
Citation in format AMSBIB
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