Investigation of Level Statistics by Generalized Brody Distribution and Maximum Likelihood Estimation Method

TL;DR

This paper extends the Brody distribution to include Poisson, GOE, and GUE limits and employs maximum likelihood estimation to analyze spectral statistics, providing more precise parameter estimates and describing transitions in level spacing.

Contribution

It introduces a generalized Brody distribution combined with ML estimation for improved spectral analysis and transition characterization in level statistics.

Findings

ML estimates yield higher precision in parameter determination.

The generalized distribution effectively captures transitions between spectral limits.

KLD measures quantify the distance to spectral limits.

Abstract

With generalizing the Brody distribution to include the Poisson, GOE and GUE limits and with employing the maximum likelihood estimation technique, the spectral statistics of different sequences were considered in the nearest neighbor spacing statistics framework. The ML-based estimated values for the parameters of generalized distribution propose more precisions in compare to the predictions of other distributions. The transition in the level spacing statistics of different systems were described by the distances of ML-based predictions for generalized distribution to three limits which determined by KLD measures.