Abstract:
We use the generating functional method for the matrix elements of second quantization operators to obtain a high-temperature expansion of the thermodynamic potential of a quantum system. This method permits isolating irreducible parts of matrices, including the particle-density matrices. We derive an equation for the full unary density matrix, which is equivalent to the variational principle for the thermodynamic potential. The thermodynamic functions and the density matrix can thus be found in the framework of the same variational problem.
Citation:
É. A. Arinstein, “Perturbation Theory for Density Matrices and the Thermodynamic Potential of a Quantum System”, TMF, 130:1 (2002), 54–63; Theoret. and Math. Phys., 130:1 (2002), 45–53
\Bibitem{Ari02}
\by \'E.~A.~Arinstein
\paper Perturbation Theory for Density Matrices and the Thermodynamic Potential of a~Quantum System
\jour TMF
\yr 2002
\vol 130
\issue 1
\pages 54--63
\mathnet{http://mi.mathnet.ru/tmf290}
\crossref{https://doi.org/10.4213/tmf290}
\zmath{https://zbmath.org/?q=an:1044.81042}
\transl
\jour Theoret. and Math. Phys.
\yr 2002
\vol 130
\issue 1
\pages 45--53
\crossref{https://doi.org/10.1023/A:1013876314504}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000173912900004}
Linking options:
https://www.mathnet.ru/eng/tmf290
https://doi.org/10.4213/tmf290
https://www.mathnet.ru/eng/tmf/v130/i1/p54
This publication is cited in the following 4 articles:
E. A. Arinshtein, “Variational Principle in Statistical Physics”, Russ. J. Phys. Chem., 96:7 (2022), 1386
Eduard A. Arinshteyn, “Variational Principle in the Quantum Statistical Theory”, JMP, 05:14 (2014), 1272
É. A. Arinstein, “The Matsubara operator for the Fröhlich model”, Theoret. and Math. Phys., 161:2 (2009), 1529–1539
Bazarov, IP, “Heat capacity calculations for systems of many particles by the Bogolyubov method”, Russian Journal of Physical Chemistry, 77:6 (2003), 901