Fractal Weyl law for quantum fractal eigenstates

Abstract

The properties of the resonant Gamow states are studied numerically in the semiclassical limit for the quantum Chirikov standard map with absorption. It is shown that the number of such states is described by the fractal Weyl law and their Husimi distributions closely follow the strange repeller set formed by classical orbits nonescaping in future times. For large matrices the distribution of escape rates converges to a fixed shape profile characterized by a spectral gap related to the classical escape rate.

4 pages, 5 figs, minor modifications, research at http://www.quantware.ups-tlse.fr/

References in corpus (5)

• Fractal Weyl laws for chaotic open systems
• Quantum-to-classical crossover of quasi-bound states in open quantum systems
• Dynamics of Anderson localization in open 3D media
• Semiclassical structure of chaotic resonance eigenfunctions
• Classical Phase Space Revealed by Coherent Light

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