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Free energy of gravitating fermions

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Abstract

We calculate rigorously, in a suitable thermodynamic limit, the free energy of a system of nonrelativistic fermions which interact with attractiver −1-potentials. It is shown that the effective field approximation becomes exact in this limit and results in the temperature-dependent Thomas-Fermi equations.

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References

  1. Dyson, J.F.: In: Statistical Physics, Phase transitions and Superfluidity, 1966 Brandeis University Summer School in Theoretical Physics, lecture notes; Dyson, F.J., Lenard, A.: J. Math. Phys.8, 423 (1967).

  2. Lebowitz, J.L., Lieb, E.H.: Phys. Rev. Letters22, 631 (1969).

    Google Scholar 

  3. Lévy-Leblond, J.-M.: J. Math. Phys.10, 806 (1969).

    Google Scholar 

  4. Thirring, W.: Z. Phys.235, 339 (1970); Hertel, P., Thirring, W.: Ann. Phys.63 (1971).

    Google Scholar 

  5. -- CERN preprint TH. 1338 (1971).

  6. Kato, T.: Perturbation theory for linear operators, Berlin-Heidelberg-New York: Springer 1966.

    Google Scholar 

  7. Maison, H.D.: Analyticity of the partition function for finite quantum systems, CERN preprint TH. 1299 (1971).

  8. Dieudonné, J.: Eléments d'analyse, Tome I, Paris: Gauthier-Villars 1969.

    Google Scholar 

  9. Simon, B.: J. Math. Phys.10, 1123 (1969).

    Google Scholar 

  10. Ruelle, D.: Statistical mechanics-rigorous results. New York: Benjamin 1961.

    Google Scholar 

  11. Bogoliubov, Jr., N.N.: Physica32, 933 (1966).

    Google Scholar 

  12. Ginibre, J.: Commun. math. Phys.8, 26 (1968).

    Google Scholar 

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On leave of absence from the University of Heidelberg, Germany.

On leave of absence from the University of Vienna, Austria.

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Hertel, P., Thirring, W. Free energy of gravitating fermions. Commun.Math. Phys. 24, 22–36 (1971). https://doi.org/10.1007/BF01907031

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  • DOI: https://doi.org/10.1007/BF01907031

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