Level Density of a Bose Gas and Extreme Value Statistics

TL;DR

This paper links the level density of a non-interacting boson gas to extreme value statistics, revealing that the distribution of excited particles follows universal laws depending on the spectrum's growth exponent.

Contribution

It introduces a novel connection between bosonic level density and extreme value theory, classifying the limiting distributions based on spectral growth.

Findings

Level density follows Gumbel, Weibull, or Fréchet distributions.

Distribution type depends on the spectrum's growth exponent.

Implications for understanding bosonic excitation spectra.

Abstract

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.