Power-law energy level spacing distributions in fractals

Askar A. Iliasov, Mikhail I. Katsnelson, and Shengjun Yuan
Phys. Rev. B 99, 075402 – Published 1 February 2019

Abstract

In this paper 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 behavior, if its energy spectrum is a limit set of piecewise linear functions. We propose that such a behavior is a general feature of fractals, which can not be described properly by random matrix theory. Several other arguments for the power-law behavior of the energy level spacing distributions are proposed.

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  • Received 6 November 2018
  • Revised 11 January 2019

DOI:https://doi.org/10.1103/PhysRevB.99.075402

©2019 American Physical Society

Physics Subject Headings (PhySH)

General Physics

Authors & Affiliations

Askar A. Iliasov1,*, Mikhail I. Katsnelson1, and Shengjun Yuan2,1,†

  • 1Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525AJ Nijmegen, The Netherlands
  • 2Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education, School of Physics and Technology, Wuhan University, Wuhan 430072, China

  • *A.Iliasov@science.ru.nl
  • s.yuan@whu.edu.cn

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Vol. 99, Iss. 7 — 15 February 2019

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