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arXiv · 1206.1856

Disorder in Gauge/Gravity Duality, Pole Spectrum Statistics and Random Matrix Theory

Omid Saremi
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Abstract

In condensed-matter, level statistics has long been used to characterize the phases of a disordered system. We provide evidence within the context of a simple model that in a disordered large-N gauge theory with a gravity dual, there exist phases where the nearest neighbor spacing distribution of the unfolded pole spectra of generic two-point correlators is Poisson. This closely resembles the localized phase of the Anderson Hamiltonian. We perform two tests on our statistical hypothesis. One is based on a statistic defined in the context of Random Matrix Theory, the so-called $\bar{Δ_3}$, or spectral rigidity, proposed by Dyson and Mehta. The second is a $χ$-squared test. In our model, the results of both tests are consistent with the hypothesis that the pole spectra of two-point functions can be at least in two distinct phases; first a regular sequence and second a completely uncorrelated sequence with a Poisson nearest neighbor spacing distribution.

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Omid Saremi. 2012-06-08. Disorder in Gauge/Gravity Duality, Pole Spectrum Statistics and Random Matrix Theory. https://arxiv.org/abs/1206.1856

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