| Issue |
Europhys. Lett.
Volume 72, Number 4, November 2005
|
|
|---|---|---|
| Page(s) | 506 - 512 | |
| DOI | https://doi.org/10.1209/epl/i2005-10278-8 | |
| Published online | 12 October 2005 | |
Fermi-Dirac statistics and the number theory
1
Instytut Fizyki im. M. Smoluchowskiego, Uniwersytet Jagielloński PL-30059 Kraków, Poland
2
Institut für Theoretische Physik, Universität Hannover D-30167 Hannover, Germany
3
ICFO-Institut de Ciències Fotòniques - E-08034 Barcelona, Spain
Received:
27
July
2005
Accepted:
21
September
2005
We relate the Fermi-Dirac statistics of an ideal Fermi gas in a harmonic trap to partitions of given integers into distinct parts, studied in number theory. Using methods of quantum statistical physics we derive analytic expressions for cumulants of the probability distribution of the number of different partitions.
PACS: 03.75.Ss – Degenerate Fermi gases / 05.30.Fk – Fermion systems and electron gas / 02.30.Mv – Approximations and expansions
© EDP Sciences, 2005
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