Level density of a bose gas and extreme value statistics.
We establish a connection between the level density of a gas of noninteracting 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, the Gumbel, Weibull, and Fréchet distributions. Implications of this result, as well as general properties of the level density at different energies, are discussed.
Comtet
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Laboratoire de Physique Théorique et Modèles Statistiques, CNRS, Université de Paris-Sud, UMR 8626, 91405 Orsay Cedex, France.
Leboeuf
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Majumdar
Satya N
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