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Fractal Weyl law for quantum fractal eigenstates

D. L. Shepelyansky
Phys. Rev. E 77, 015202(R) – Published 28 January 2008

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.

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  • Received 14 September 2007

DOI:https://doi.org/10.1103/PhysRevE.77.015202

©2008 American Physical Society

Authors & Affiliations

D. L. Shepelyansky

  • Laboratoire de Physique Théorique, UMR 5152 du CNRS, Université Toulouse III, 31062 Toulouse, France

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Issue

Vol. 77, Iss. 1 — January 2008

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