Fractal Weyl law for quantum fractal eigenstates
Disordered Systems and Neural Networks
2008-01-29 v2 Mesoscale and Nanoscale Physics
Mathematical Physics
math.MP
Chaotic Dynamics
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.
Keywords
Cite
@article{arxiv.0709.2336,
title = {Fractal Weyl law for quantum fractal eigenstates},
author = {D. L. Shepelyansky},
journal= {arXiv preprint arXiv:0709.2336},
year = {2008}
}
Comments
4 pages, 5 figs, minor modifications, research at http://www.quantware.ups-tlse.fr/