Advertisement

Communications in Mathematical Physics

, Volume 78, Issue 1, pp 83–98 | Cite as

Gravitating fermions in an infinite configuration space

  • A. Pflug
Article

Abstract

For a system of (infinitely many) nonrelativistic gravitating fermions described rigorously by Thomas-Fermi theory, a nontrivial limit of infinite configuration volume |∧| is shown to exist for the microcanonical free energy, and for the entropy divided by log|∧|. It can be calculated explicitly using the scaling behaviour of the (ground state). Thomas-Fermi equation and shows a phase transition at zero energy. For all (possible) negative energies, the heat capacity of the infinitely extended system is negative and a nonzero fraction of the particles is in the condensed phase.

Keywords

Entropy Neural Network Phase Transition Free Energy Statistical Physic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Auchmuty, J., Beals, R.: Arch. Ration Mech. Anal.43, 255–271 (1971)CrossRefGoogle Scholar
  2. 2.
    Baumgartner, B.: Commun. Math. Phys.48, 207–213 (1976)CrossRefGoogle Scholar
  3. 3.
    Baumgartner, B.: Commun. Math. Phys.75, 25–41 (1980)Google Scholar
  4. 4.
    Hertel, P., Narnhofer, H., Thirring, W.: Commun. Math. Phys.28, 159–176 (1972)CrossRefGoogle Scholar
  5. 5.
    Hertel, P., Thirring, W.: Commun. Math. Phys.24, 22–36 (1971)Google Scholar
  6. 6.
    Hertel, P., Thirring, W.: Thermodynamic instability of a system of gravitating fermions. In: Quanten und Felder. Dürr, H.P. (ed.), Braunschweig: Vieweg 1971Google Scholar
  7. 7.
    Lieb, E., Simon, B.: Adv. Math.23, 22–116 (1977)CrossRefGoogle Scholar
  8. 8.
    Messer, J.: Z. Phys. B33, 313–316 (1979)CrossRefGoogle Scholar
  9. 9.
    Ruelle, D.: Statistical mechanics, rigorous results. New York, Amsterdam: Benjamin 1969Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • A. Pflug
    • 1
  1. 1.Institut für Theoretische PhysikUniversität WienWienAustria

Personalised recommendations