Statistics of eigenvectors in the deformed Gaussian unitary ensemble of random matrices
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 the Gaussian unitary ensemble and W is a deterministic diagonal matrix with positive entries. Using the supersymmetry approach we calculate analytically the m...
| Main Authors: | , |
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| Format: | Article |
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IOP
2016
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| Online Access: | https://eprints.nottingham.ac.uk/44637/ |
| Summary: | 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 the 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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