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.
- Received 6 November 2018
- Revised 11 January 2019
DOI:https://doi.org/10.1103/PhysRevB.99.075402
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