Generalized Binomial Probability Distributions attached to Landau levels on the Riemann sphere

TL;DR

This paper introduces a new family of generalized binomial probability distributions linked to Landau levels on the Riemann sphere, using generalized coherent states, and explores their statistical properties and photon number statistics.

Contribution

It presents a novel construction of generalized binomial distributions associated with Landau levels on the Riemann sphere, including explicit statistical parameters and applications to photon statistics.

Findings

Explicit statistical parameters derived for the distributions

Photon number statistics analyzed for the coherent states

New connection between Landau levels and probability distributions

Abstract

A family of generalized binomial probability distributions attached to Landau levels on the Riemann sphere is introduced by constructing a kind of generalized coherent states. Their main statistical parameters are obtained explicitly. As application, photon number statistics related to coherent states under consideration are discussed.