The statistical distribution for the number of bosons in a specified subsystem of a finite-dimensional multilevel system is obtained and investigated under conditions for which the total number of particles is a random variable characterized by the Poisson distribution. The resulting hyper-Poisson distribution is determined by the confluent hypergeometric function and contains as its particular limiting cases the Poisson distribution, as well as the single-mode and multimode thermal distributions. The developed model can be efficiently used to describe the thermal characteristics of bounded quantum systems, as well as in the problems of statistical reconstruction of optical quantum states, processes, and detectors.

中文翻译：

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超泊松光子统计

在粒子总数为以泊松分布为特征的随机变量的条件下，获得并研究了有限维多级系统指定子系统中玻色子数的统计分布。最终的超泊松分布由合流超几何函数确定，并且包含泊松分布以及单模和多模热分布作为其特殊的极限情况。所开发的模型可以有效地用于描述有界量子系统的热特性，以及光学量子态，过程和检测器的统计重建问题。