Critical Level Statistics of the Fibonacci Model

Details Critical Level Statistics of the Fibonacci Model Critical Level Statistics of the Fibonacci Model

2004-10-08

arxiv.org/abs/cond-mat/0410187v1

Physics

Condensed Matter

Statistical Mechanics

7 pages

Scientific paper

10.1103/PhysRevB.71.245120

We numerically analyze spectral properties of the Fibonacci model which is a one-dimensional quasiperiodic system. We find that the energy levels of this model have the distribution of the band widths $w$ obeys $P_B(w)\sim w^{\alpha}$ $(w\to 0)$ and $P_B(w) \sim e^{-\beta w}$ $(w\to\infty)$, the gap distribution $P_G(s)\sim s^{-\delta}$ $(s\to 0)$ ($\alpha,\beta,\delta >0$) . We also compare the results with those of multi-scale Cantor sets. We find qualitative differences between the spectra of the Fibonacci model and the multi-scale Cantor sets.

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