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2018

Eigenfunction distribution for the Rosenzweig-Porter model

Bogomolny, E., Sieber, M.

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The statistical distribution of eigenfunctions for the Rosenzweig-Porter model is derived for the region where eigenfunctions have fractal behaviour.

The result is based on simple physical ideas and leads to transparent explicit formulas which agree very well with numerical calculations.
It constitutes a rare case where a non-trivial eigenfunction distribution is obtained in a closed form.

Eigenfunction distribution for the Rosenzweig-Porter model · Around

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Higher Transcendental Functions
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E. P. Wigner, Ann. Math. 62
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N. Rosenzweig and C. E. Porter, Phys. Rev. 120
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A. D. Mirlin, Y. V. Fyodorov, F.-M. Dittes, J. Quezada, and T. H. Seligman, Phys. Rev. E 54
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