Linearized spectral decimation in fractals
Disordered Systems and Neural Networks
2020-09-02 v1 Mesoscale and Nanoscale Physics
Quantum Physics
Abstract
In this article we study the energy level spectrum of fractals which have block-hierarchical structures. We develop a method to study the spectral properties in terms of linearization of spectral decimation procedure and verify it numerically. Our approach provides qualitative explanations for various spectral properties of self-similar graphs within the theory of dynamical systems, including power-law level-spacing distribution, smooth density of states and effective chaotic regime.
Cite
@article{arxiv.2006.02339,
title = {Linearized spectral decimation in fractals},
author = {Askar A. Iliasov and Mikhail I. Katsnelson and Shengjun Yuan},
journal= {arXiv preprint arXiv:2006.02339},
year = {2020}
}