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Linearized spectral decimation in fractals
Askar A. Iliasov, Mikhail I. Katsnelson, Shengjun Yuan
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 linearizat…
Hall conductivity of Sierpinski carpet
Askar A. Iliasov, Mikhail I. Katsnelson, Shengjun Yuan
We calculate the Hall conductivity of a Sierpinski carpet using Kubo-Bastin formula. The quantization of Hall conductivity disappears when we increase the depth of the fractal. The…
Power-law energy level-spacing distributions in fractals
Askar A. Iliasov, Mikhail I. Katsnelson, Shengjun Yuan
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 behaviou…