Teoreticheskaya i Matematicheskaya Fizika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Teoreticheskaya i Matematicheskaya Fizika, 1990, Volume 82, Number 3, Pages 410–427 (Mi tmf5721)  

Quasiparticle treatment of quantum-mechanical perturbation theory in the free electron gas

A. I. Voropinov
References:
Abstract: The correlation energy of the free electron gas is investigated. The point of departure is Wigner's idea of selective summation of the perturbation-theory series for the ground-state energy. The introduction of a quasiparticle operator (with a quasiparticle understood as representing momentum propagation in the system) makes possible the resummation of the perturbation-theory series in such a way that the order of the terms is determined, not by the number of different particles that participate in an interaction, but by the number of different lines (momentum transfers). The matrix elements of the quasiparticle operator are obtained as the solution of an integral equation determined in the Macke–Tamm–Dankoff approximation and the RPA. The first order of the quasiparticle perturbation theory series (it includes the Hartree–Fock exchange energy) is simply the sum of the energies of the quasiparticles. The obtained expressions are identical to the results of other theories. The second order corresponds to exchange interaction of the quasiparticles. For it, numerical calculations are made in the range of $r_S$ from 0.1 to 10 a. u. Comparison with the analogous results obtained in the $e^S$ method has shown the inadequacy of the $e^S$ method, in which the best successes have been achieved in the investigation of the correlation energy of the free electron gas. In the case of high densities (small $r_S$) the quasiparticle exchange interaction tends to the particle exchange interaction, which was first calculated by Gell-Mann and Brueckner and for which an exact value was obtained by Onsager and collaborators. The results for the total correlation energy (the sum of the first and second terms but with the Hartree–Fock exchange energy subtracted) agrees better with the results of Hubbard and Nozières and Pines than with other results.
Received: 16.01.1989
English version:
Theoretical and Mathematical Physics, 1990, Volume 82, Issue 3, Pages 288–300
DOI: https://doi.org/10.1007/BF01029223
Bibliographic databases:
Language: Russian
Citation: A. I. Voropinov, “Quasiparticle treatment of quantum-mechanical perturbation theory in the free electron gas”, TMF, 82:3 (1990), 410–427; Theoret. and Math. Phys., 82:3 (1990), 288–300
Citation in format AMSBIB
\Bibitem{Vor90}
\by A.~I.~Voropinov
\paper Quasiparticle treatment of~quantum-mechanical perturbation theory in~the free electron gas
\jour TMF
\yr 1990
\vol 82
\issue 3
\pages 410--427
\mathnet{http://mi.mathnet.ru/tmf5721}
\transl
\jour Theoret. and Math. Phys.
\yr 1990
\vol 82
\issue 3
\pages 288--300
\crossref{https://doi.org/10.1007/BF01029223}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1990EB42600009}
Linking options:
  • https://www.mathnet.ru/eng/tmf5721
  • https://www.mathnet.ru/eng/tmf/v82/i3/p410
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024