Non-Monotone Characteristic of Spectral Statistics in the Transition between Poisson and Gauss

Details Non-Monotone Characteristic of Spectral Statistics in the Transition between Poisson and Gauss Non-Monotone Characteristic of Spectral Statistics in the Transition between Poisson and Gauss

1998-08-03

arxiv.org/abs/cond-mat/9808028v1

Physics

Condensed Matter

10 Revtex pages, 3 PS figures

Scientific paper

We have computed the spectral number variances of an extended random matrix ensemble predicted by Guhr's supersymmetry formula, showing a non-monotone increase of the curves that arises from an "overshoot" of the two-level correlation function above unity. On the basis of the most general form of $N$-level joint distribution that meets sound probabilistic conditions on matrix spaces, the above characteristic may be attributed to the {\it attractiveness} of the pair potential in long range($E >$ Thouless energy) of the underlying level gas. The approach of level dynamics indicates that the result is "anti-screening" of the level repulsion in short-range statistics of the usual random matrix prediction until the joint level distribution undergoes a phase transition (the Anderson transition).

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