Linearized spectral decimation in fractals
Askar A. Iliasov, Mikhail I. Katsnelson, Shengjun Yuan
TL;DR
This paper introduces a linearization method for spectral decimation to analyze the energy spectra of fractals with hierarchical structures, providing insights into their spectral properties through dynamical systems theory.
Contribution
It develops a novel linearization approach to spectral decimation for fractals, verified numerically, linking spectral properties to dynamical systems concepts.
Findings
Power-law level-spacing distribution observed
Smooth density of states confirmed
Effective chaotic regime identified
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.
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