Skip to main content
SpringerLink
Log in

On the Coulomb energy of a finite-temperature electron gas

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

We rederive the Coulomb expansion of the electron gas average energy at finite temperature, starting from scratch, i.e., using only the framework of the grand canonical ensemble and not the finite-T Green's function formalism. We recover the analytical expressions of the exchange and correlation energy in both the high-T and theT=0 limits. We explicitly show the origin of the crossover of the correlation energy leading term frome 4 lne 2 at zero temperature toe 3 at finiteT. We also discuss the relative importance of exchange and correlation in both limits.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Gell-Mann and K. A. Brueckner,Phys. Rev. 106:364 (1957).

    Article  Google Scholar 

  2. J. Hubbard,Proc. Soc. Lond. A 243:336 (1957).

    Google Scholar 

  3. A. L. Fetter and J. D. Walecka,Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 1971).

    Google Scholar 

  4. G. D. Mahan,Many-Particle Physics (Plenum Press, New York, 1981).

    Google Scholar 

  5. D. M. Ceperley,Phys. Rev. B 18:3126 (1978); D. M. Ceperley and B. J. Alder.Phys. Rev. Lett. 45:566 (1980).

    Article  Google Scholar 

  6. A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski,Methods of Quantum Field Theory in Statistical Physics (Prentice-Hall, Englewood Cliffs, New Jersey, 1963).

    Google Scholar 

  7. H. E. De Witt,J. Math. Phys. 3:1216 (1962).

    Article  Google Scholar 

  8. M. W. C. Dharma-Wardana and R. Taylor,J. Phys. C 14:629 (1981).

    Google Scholar 

  9. F. Perrot and M. W. C. Dharma-Wardana,Phys. Rev. A 30:2619 (1984).

    Article  Google Scholar 

  10. S. Tanaka, S. Mitake, and S. Ichimaru,Phys. Rev. A 32:2619 (1985).

    Google Scholar 

  11. R. G. Dandrea, N. M. Ashcroft, and A. E. Carlsson,Phys. Rev. B 34:2097 (1986).

    Article  Google Scholar 

  12. L. D. Landau and E. M. Lifchitz,Statistical Physics (Pergamon Press, London, 1959), Chapter V.

    Google Scholar 

  13. B. Diu, C. Guthmann, D. Lederer, and B. Roulet,Physique Statistique (Hermann, Paris, 1989), Chapter V.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Groupe de Physique des Solides, Université Pierre et Marie Curie et Université Paris VII, 2 place Jussieu, 75005, Paris, France

    Odile Betbeder-Matibet & Monique Combescot

  2. Laboratoire d'Optique appliquée, ENSTA, Ecole Polytechnique, Batterie de l'Yvette, 91120, Palaiseau, France

    Monique Combescot

Authors
  1. Odile Betbeder-Matibet
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Monique Combescot
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Betbeder-Matibet, O., Combescot, M. On the Coulomb energy of a finite-temperature electron gas. J Stat Phys 75, 953–969 (1994). https://doi.org/10.1007/BF02186752

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02186752

Key Words

Search

Navigation