Analysis of generalized negative binomial distributions attached to hyperbolic Landau levels
Abstract
To each hyperbolic Landau level of the Poincar\'e disc is attached a generalized negative binomial distribution. In this paper, we compute the moment generating function of this distribution and supply its decomposition as a perturbation of the negative binomial distribution by a finitely-supported measure. Using the Mandel parameter, we also discuss the nonclassical nature of the associated coherent states. Next, we determine the L\'evy-Kintchine decomposition its characteristic function when the latter does not vanish and deduce that it is quasi-infinitely divisible except for the lowest hyperbolic Landau level corresponding to the negative binomial distribution. By considering the total variation of the obtained quasi-L\'evy measure, we introduce a new infinitely-divisible distribution for which we derive the characteristic function.
Keywords
Cite
@article{arxiv.1602.01371,
title = {Analysis of generalized negative binomial distributions attached to hyperbolic Landau levels},
author = {Hassan Chhaiba and Nizar Demni and Zouhair Mouayn},
journal= {arXiv preprint arXiv:1602.01371},
year = {2016}
}