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arXiv · 1811.01659

Power-law energy level-spacing distributions in fractals

Askar A. Iliasov·Mikhail I. Katsnelson·Shengjun Yuan
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Abstract

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.

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Askar A. Iliasov, Mikhail I. Katsnelson, Shengjun Yuan. 2018-11-06. Power-law energy level-spacing distributions in fractals. https://doi.org/10.1103/physrevb.99.075402

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