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arXiv · 1511.09345

Statistics of eigenvectors in the deformed Gaussian unitary ensemble of random matrices

Kevin Truong·Alexander Ossipov
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Abstract

We study eigenvectors in the deformed Gaussian unitary ensemble of random matrices $H=W\tilde{H}W$, where $\tilde{H}$ is a random matrix from Gaussian unitary ensemble and $W$ is a deterministic diagonal matrix with positive entries. Using the supersymmetry approach we calculate analytically the moments and the distribution function of the eigenvectors components for a generic matrix $W$. We show that specific choices of $W$ can modify significantly the nature of the eigenvectors changing them from extended to critical to localized. Our analytical results are supported by numerical simulations.

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Kevin Truong, Alexander Ossipov. 2015-11-30. Statistics of eigenvectors in the deformed Gaussian unitary ensemble of random matrices. https://doi.org/10.1088/1751-8113%2F49%2F14%2F145005

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