Level Density of a Bose Gas and Extreme Value Statistics

Details Level Density of a Bose Gas and Extreme Value Statistics Level Density of a Bose Gas and Extreme Value Statistics

2006-10-16

arxiv.org/abs/cond-mat/0610411v1

Phys. Rev. Lett. 98, 070404 (2007)

Physics

Condensed Matter

Statistical Mechanics

4 pages, no figures

Scientific paper

10.1103/PhysRevLett.98.070404

We establish a connection between the level density of a gas of non-interacting bosons and the theory of extreme value statistics. Depending on the exponent that characterizes the growth of the underlying single-particle spectrum, we show that at a given excitation energy the limiting distribution function for the number of excited particles follows the three universal distribution laws of extreme value statistics, namely Gumbel, Weibull and Fr\'echet. Implications of this result, as well as general properties of the level density at different energies, are discussed.

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