Random discrete Schrödinger operators from Random Matrix Theory

Details Random discrete Schrödinger operators from Random Matrix Theory Random discrete Schrödinger operators from Random Matrix Theory

2005-07-15

arxiv.org/abs/math-ph/0507036v2

Physics

Mathematical Physics

9 pages, 0 figures

Scientific paper

We investigate random, discrete Schr\"odiner operators which arise naturally in the theory of random matrices, and depend parametrically on Dyson's Coulomb gas inverse temperature $\beta$. They belong to the class of "critical" random Schr\"odiner operators with random potentials which diminish as $|x|^{-{1/2}}$. We show that as a function of $\beta$ their eigenstates undergo a transition from extended ($\beta \ge 2 $) to power-law localized ($0 < \beta < 2$).

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