The intermediate level statistics in dynamically localized chaotic eigenstates

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 Poincaré 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.

6 pages, 4 figures (published in EPL)

References in corpus (3)

• Quantum mushroom billiards
• Expanded boundary integral method and chaotic time-reversal doublets in quantum billiards
• Dynamical localization in chaotic systems: spectral statistics and localization measure in the kicked rotator as a paradigm for time-dependent and time-independent systems

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• Aspects of diffusion in the stadium billiard
• Statistical properties of the localization measure in a finite-dimensional model of the quantum kicked rotator
• Further results on the power-law decay of the fraction of the mixed eigenstates in kicked-top model with mixed-type classical phase space
• PT -symmetry breaking and universal spectral statistics in quantum kicked rotors