Impact of localization on Dyson's circular ensemble

Details Impact of localization on Dyson's circular ensemble Impact of localization on Dyson's circular ensemble

1995-10-02

arxiv.org/abs/cond-mat/9510005v1

Physics

Condensed Matter

To be published in J. Phys. A

Scientific paper

10.1088/0305-4470/28/21/005

A wide variety of complex physical systems described by unitary matrices have been shown numerically to satisfy level statistics predicted by Dyson's circular ensemble. We argue that the impact of localization in such systems is to provide certain restrictions on the eigenvalues. We consider a solvable model which takes into account such restrictions qualitatively and find that within the model a gap is created in the spectrum, and there is a transition from the universal Wigner distribution towards a Poisson distribution with increasing localization.

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