Europhys. Lett.
Volume 72, Number 4, November 2005
Page(s) 506 - 512
Section General
Published online 12 October 2005
Europhys. Lett., 72 (4), pp. 506-512 (2005)
DOI: 10.1209/epl/i2005-10278-8

Fermi-Dirac statistics and the number theory

Anna Kubasiak1, Jaroslaw K. Korbicz2, Jakub Zakrzewski1 and Maciej Lewenstein2, 3

1  Instytut Fizyki im. M. Smoluchowskiego, Uniwersytet Jagiellonski 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
published online 12 October 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.

03.75.Ss - Degenerate Fermi gases.
05.30.Fk - Fermion systems and electron gas.
02.30.Mv - Approximations and expansions.

© EDP Sciences 2005