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Level-spacing distribution of a fractal matrix

D. E. Katsanos·S. N. Evangelou
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Abstract

We diagonalize numerically a Fibonacci matrix with fractal Hilbert space structure of dimension $d_{f}=1.8316...$ We show that the density of states is logarithmically normal while the corresponding level-statistics can be described as critical since the nearest-neighbor distribution function approaches the intermediate semi-Poisson curve. We find that the eigenvector amplitudes of this matrix are also critical lying between extended and localized.

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D. E. Katsanos, S. N. Evangelou. 2001-11-06. Level-spacing distribution of a fractal matrix. https://doi.org/10.1016/s0375-9601(01)00593-x

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