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

Truong, K.; Ossipov, A.

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 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.

Citation

Truong, K., & Ossipov, A. (2016). Statistics of eigenvectors in the deformed Gaussian unitary ensemble of random matrices. Journal of Physics A: Mathematical and Theoretical, 49(14), https://doi.org/10.1088/1751-8113/49/14/145005

• Journal Article Type: Article
• Acceptance Date: Jan 25, 2016
• Publication Date: Feb 23, 2016
• Deposit Date: Aug 4, 2017
• Publicly Available Date: Aug 4, 2017
• Journal: Journal of Physics A: Mathematical and Theoretical
• Print ISSN: 1751-8113
• Electronic ISSN: 1751-8121
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 49
• Issue: 14
• DOI: https://doi.org/10.1088/1751-8113/49/14/145005
• Public URL: https://nottingham-repository.worktribe.com/output/775525
• Publisher URL: http://iopscience.iop.org/article/10.1088/1751-8113/49/14/145005/meta