Calculating the Mandel parameter for an oscillator-like system generated by generalized Chebyshev polynomials

TL;DR

This paper calculates the Mandel parameter for an oscillator-like system based on generalized Chebyshev polynomials to analyze its excitation statistics deviation from Poisson distribution.

Contribution

It introduces a method to compute the Mandel parameter for systems generated by generalized Chebyshev polynomials, extending previous work on oscillator-like systems.

Findings

Mandel parameter computed for the system

Deviation from Poisson statistics characterized

Extension of previous oscillator system analyses

Abstract

In this paper, we calculate the Mandel parameter $Q_M$ for an oscillator-like system generated by generalized Chebyshev polynomials \cite{01}, \cite{02}, \cite{03}. The sign of the Mandel parameter $Q_M$ characterizes the deviation of the excitation statistics from the Poisson one. This work is a continuation of our works \cite{04}, \cite{05}.