The intermediate level statistics in dynamically localized chaotic eigenstates

TL;DR

This paper shows that the level spacing distribution in dynamically localized chaotic eigenstates follows the Brody distribution, indicating fractional level repulsion, confirmed through high-energy analysis of two chaotic systems.

Contribution

It demonstrates that the Brody distribution accurately describes level spacings in high-energy localized chaotic eigenstates, extending previous understanding to very high energies.

Findings

Brody distribution fits the level spacing data well.

High-energy separation of regular and chaotic states confirms Berry-Robnik picture.

Analysis performed on over half a million eigenstates at high energies.

Abstract

We demonstrate that the energy or quasienergy level spacing distribution in dynamically localized chaotic eigenstates is excellently described by the Brody distribution, displaying the fractional power law level repulsion. This we show in two paradigmatic systems, namely for the fully chaotic eigenstates of the kicked rotator at K=7, and for the chaotic eigenstates in the mixed-type billiard system (Robnik 1983), after separating the regular and chaotic eigenstates by means of the Poincar\'e Husimi function, at very high energies with great statistical significance (587654 eigenstates, starting at about 1.000.000 above the ground state). This separation confirms the Berry-Robnik picture, and is performed for the first time at such high energies.