Thermodynamics and occupation numbers of a Fermi gas in the canonical ensemble

American Journal of Physics

Volumn 68, Issue 11, 2000, Pages 1032-1037

  Schonhammer K ^a  

^a UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034369154     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1286116     Document Type: Article

References (13)

1. R. Denton, B. Mühlschlegel, and D. J. Scalapino, "Thermodynamic properties of electrons in small metal particles," Phys. Rev. B 7, 3589-3607 (1973).
2. K. Schönhammer and V. Meden, "Fermion-boson transmutation and comparison of statistical ensembles in one dimension," Am. J. Phys. 64, 1168-1176 (1996).
3. J. Arnaud, J. M. Boe, L. Chusseau, and F. Philippe, "Illustration of Fermi-Dirac statistics," Am. J. Phys. 67, 215-221 (1999).
4. While this approach is not very elegant for the case of noninteracting electrons it allows, in contrast to the other methods discussed in this paper, the extension of these calculations to the case of interacting electrons (Ref. 12).
5. H. Schmidt, "Eine einfache Herleitung der Verteilungsfunktionen für Bose-und Fermi-Statistik," Z. Phys. 134, 430-431 (1953).
6. H. Schmidt, "A simple derivation of distribution functions for Bose and Fermi statistics," Am. J. Phys. 57, 1150-1151 (1989).
7. R. Baierlein, Thermal Physics (Cambridge U.P., Cambridge, 1999). I learned of Refs. 5 and 6 while reading this nice new textbook.
8. P. Borrmann, J. Harting, O. Mülken, and E. Hilf, "Calculation of thermodynamic properties of finite Bose-Einstein systems," Phys. Rev. A 60, 1519-1522 (1999).
9. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart and Winston, New York, 1976).
10. F. In this paper the (low temperature) heat capacity per unit length and not per particle was calculated. If this is taken into account Eq. (13) of Ref. 2 corresponds to Eq. (A6) of the present paper.
11. in Ref. 3 half integer indices are introduced in order to make Eq. (23) look more symmetrical. In Eq. (24) this amounts to the replacement l→l - 1/2.
12. F. D. Haldane, "Luttinger liquid theory of one dimensional quantum fluids. I. Properties of the Luttinger model and their extension to the general 1D interacting spinless Fermi gas," J. Phys. C 14, 2585-2919 (1981). For a more pedagogical calculation in the spirit of Ref. 2 see: K. Schönhammer, "Interacting fermions in one dimension: The Tomonaga-Luttinger model," cond-mat/9710330, 1-21 (1997).
13. F. D. Haldane, "Luttinger liquid theory of one dimensional quantum fluids. I. Properties of the Luttinger model and their extension to the general 1D interacting spinless Fermi gas," J. Phys. C 14, 2585-2919 (1981). For a more pedagogical calculation in the spirit of Ref. 2 see: K. Schönhammer, "Interacting fermions in one dimension: The Tomonaga-Luttinger model," cond-mat/9710330, 1-21 (1997).