双曲朗道能级的广义负二项分布分析
Analysis of generalized negative binomial distributions attached to hyperbolic Landau levels
摘要：
庞加莱圆盘的每一个双曲朗道能级都有一个广义负二项分布。本文计算了该分布的矩母函数，并将其分解作为负二项分布在有限支撑测度下的扰动。利用Mandel参数，我们还讨论了关联相干态的非经典性质。其次，当Lévy-Kintchine分解的特征函数不为零时，我们确定了Lévy-Kintchine分解的特征函数，并推导出除了对应于负二项分布的最低双曲朗道水平外，Lévy-Kintchine分解是准无限可分的.通过考虑所得到的拟Lévy测度的全变差，我们引入了一个新的无穷可分分布，并导出了它的特征函数.
英文摘要：
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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