Comtet A, Leboeuf P, Majumdar Satya N
Laboratoire de Physique Théorique et Modèles Statistiques, CNRS, Université de Paris-Sud, UMR 8626, 91405 Orsay Cedex, France.
Phys Rev Lett. 2007 Feb 16;98(7):070404. doi: 10.1103/PhysRevLett.98.070404. Epub 2007 Feb 15.
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.
我们在非相互作用玻色子气体的能级密度与极值统计理论之间建立了联系。根据表征基础单粒子谱增长的指数，我们表明在给定的激发能量下，激发粒子数的极限分布函数遵循极值统计的三个通用分布定律，即耿贝尔分布、威布尔分布和弗雷歇分布。讨论了这一结果的影响以及不同能量下能级密度的一般性质。
