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arXiv · 1602.01371

Analysis of generalized negative binomial distributions attached to hyperbolic Landau levels

Hassan Chhaiba·Nizar Demni·Zouhair Mouayn
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Abstract

To each hyperbolic Landau level of the Poincaré 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 Lévy-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-Lévy measure, we introduce a new infinitely-divisible distribution for which we derive the characteristic function.

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Hassan Chhaiba, Nizar Demni, Zouhair Mouayn. 2016-02-03. Analysis of generalized negative binomial distributions attached to hyperbolic Landau levels. https://doi.org/10.1063/1.4958724

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