Linearized spectral decimation in fractals
- Resource Type
- Working Paper
- Authors
- Iliasov, Askar A.; Katsnelson, Mikhail I.; Yuan, Shengjun
- Source
- Phys. Rev. B 102, 075440 (2020)
- Subject
- Condensed Matter - Disordered Systems and Neural Networks
Condensed Matter - Mesoscale and Nanoscale Physics
Quantum Physics
- Language
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.