Level-spacing distribution of a fractal matrix

Details Level-spacing distribution of a fractal matrix Level-spacing distribution of a fractal matrix

2001-11-06

arxiv.org/abs/cond-mat/0111080v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

6 pages, Latex file, 4 postscript files, published in Phys. Lett. A289 pp 183-7 (2001)

Scientific paper

10.1016/S0375-9601(01)00593-X

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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