Analysis of generalized negative binomial distributions attached to hyperbolic Landau levels

Hassan Chhaiba, Nizar Demni, Zouhair Mouayn

Research output: Contribution to journalArticlepeer-review

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 atomic 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 derive a Lévy-Khintchine-type representation of 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. Published by AIP Publishing.

Original languageEnglish (US)
Article number0721031
JournalJournal of Mathematical Physics
Volume57
Issue number7
DOIs
StatePublished - Jul 1 2016

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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