On the spectral unfolding of chaotic and mixed systems

TL;DR

This paper investigates how the spectral unfolding process affects the analysis of spectral fluctuations in chaotic and mixed quantum systems, highlighting the impact of extreme eigenvalues on the sensitivity of statistical measures.

Contribution

It identifies the role of extreme eigenvalues in causing sensitivity to polynomial degree in spectral unfolding, improving understanding of spectral analysis in quantum chaos.

Findings

Extreme eigenvalues influence spectral unfolding sensitivity.

Sensitivity to polynomial degree affects chaos detection.

Proper handling of eigenvalues improves spectral analysis accuracy.

Abstract

Random matrix theory (RMT) provides a framework to study the spectral fluctuations in physical systems. RMT is capable of making predictions for the fluctuations only after the removal of the secular properties of the spectrum. Spectral unfolding procedure is used to separate the local level fluctuations from overall energy dependence of the level separation. The unfolding procedure is not unique. Several studies showed that statistics of long-term correlation in the spectrum are very sensitive to the choice of the unfolding function in polynomial unfolding. This can give misleading results regarding the chaoticity of quantum systems. In this letter, we consider the spectra of ordered eigenvalues of large random matrices. We show that the main cause behind the reported sensitivity to the unfolding polynomial degree is the inclusion of specific extreme eigenvalue(s) in the unfolding process.