The Relevance of Brody Level Spacing Distribution in Dynamically Localized Chaotic Eigenstates

Abstract

We study dynamically localized chaotic eigenstates in the finite dimensional quantum kicked rotator as a paradigm of Floquet systems and in a billiard system of the mixed-type (Robnik 1983) as a paradigm of time-independent Hamilton systems. In the first case we study the spectrum of quasienergies, in the second one the energy spectrum. In the kicked rotator we work in the entirely chaotic regime at K = 7, whilst in the billiard we use the Poincaré Husimi functions (on the Poincaré Birkhoff surface of section) to separate the regular and chaotic eigenstates, and then perform the analysis of 587654 high-lying chaotic eigenstates (starting at about 1.000.000 above the ground state). In both cases we show that the Brody distribution excellently describes the level spacing distribution, with an unprecedented accuracy and statistical significance. The Berry-Robnik picture of separating the regular and chaotic levels in the case of the billiard is also confirmed.