Power-law energy level-spacing distributions in fractals
Disordered Systems and Neural Networks
2019-02-06 v2 Mesoscale and Nanoscale Physics
Quantum Physics
Abstract
In this article we investigate the energy spectrum statistics of fractals at the quantum level. We show that the energy-level distribution of a fractal follows a power-law behaviour, if its energy spectrum is a limit set of piece-wise linear functions. We propose that such a behaviour is a general feature of fractals, which can not be described properly by random matrix theory. Several other arguments for the power-law behaviour of the energy level-spacing distributions are proposed.
Keywords
Cite
@article{arxiv.1811.01659,
title = {Power-law energy level-spacing distributions in fractals},
author = {Askar A. Iliasov and Mikhail I. Katsnelson and Shengjun Yuan},
journal= {arXiv preprint arXiv:1811.01659},
year = {2019}
}