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...

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Main Authors: Truong, K., Ossipov, A.
Format: Article
Published: IOP 2016
Online Access:https://eprints.nottingham.ac.uk/44637/
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author Truong, K.
Ossipov, A.
author_facet Truong, K.
Ossipov, A.
author_sort Truong, K.
building Nottingham Research Data Repository
collection Online Access
description 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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spelling nottingham-446372020-05-04T17:35:56Z https://eprints.nottingham.ac.uk/44637/ Statistics of eigenvectors in the deformed Gaussian unitary ensemble of random matrices Truong, K. Ossipov, A. 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. IOP 2016-02-23 Article PeerReviewed Truong, K. and Ossipov, A. (2016) Statistics of eigenvectors in the deformed Gaussian unitary ensemble of random matrices. Journal of Physics A: Mathematical and Theoretical, 49 (14). p. 145005. ISSN 1751-8121 http://iopscience.iop.org/article/10.1088/1751-8113/49/14/145005/meta doi:10.1088/1751-8113/49/14/145005 doi:10.1088/1751-8113/49/14/145005
spellingShingle Truong, K.
Ossipov, A.
Statistics of eigenvectors in the deformed Gaussian unitary ensemble of random matrices
title Statistics of eigenvectors in the deformed Gaussian unitary ensemble of random matrices
title_full Statistics of eigenvectors in the deformed Gaussian unitary ensemble of random matrices
title_fullStr Statistics of eigenvectors in the deformed Gaussian unitary ensemble of random matrices
title_full_unstemmed Statistics of eigenvectors in the deformed Gaussian unitary ensemble of random matrices
title_short Statistics of eigenvectors in the deformed Gaussian unitary ensemble of random matrices
title_sort statistics of eigenvectors in the deformed gaussian unitary ensemble of random matrices
url https://eprints.nottingham.ac.uk/44637/
https://eprints.nottingham.ac.uk/44637/
https://eprints.nottingham.ac.uk/44637/