Power-law energy level-spacing distributions in fractals
- Resource Type
- Working Paper
- Authors
- Iliasov, Askar A.; Katsnelson, Mikhail I.; Yuan, Shengjun
- Source
- Phys. Rev. B 99, 075402 (2019)
- Subject
- Condensed Matter - Disordered Systems and Neural Networks
Condensed Matter - Mesoscale and Nanoscale Physics
Quantum Physics
- Language
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.