Higher Order Correlations in Quantum Chaotic Spectra

TL;DR

This paper investigates higher order spectral correlations in quantum chaotic systems using semiclassical methods, extending the understanding beyond second order effects and testing the limits of random matrix theory's applicability.

Contribution

It provides the first semiclassical analysis of higher order spectral correlations in quantum maps, advancing the understanding of quantum chaos beyond second order.

Findings

Higher order correlations reveal limitations of random matrix theory.

Semiclassical calculations successfully extend spectral analysis.

Results applicable to both quantum maps and time-independent systems.

Abstract

The statistical properties of the quantum chaotic spectra have been studied, so far, only up to the second order correlation effects. The numerical as well as the analytical evidence that random matrix theory can successfully model the spectral fluctuatations of these systems is available only up to this order. For a complete understanding of spectral properties it is highly desirable to study the higher order spectral correlations. This will also inform us about the limitations of random matrix theory in modelling the properties of quantum chaotic systems. Our main purpose in this paper is to carry out this study by a semiclassical calculation for the quantum maps; however results are also valid for time-independent systems.