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

K Truong, A Ossipov
2016 Journal of Physics A: Mathematical and Theoretical  
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
more » ... tors changing them from extended to critical to localized. Our analytical results are supported by numerical simulations.
doi:10.1088/1751-8113/49/14/145005 fatcat:l4ddphaakrd23jcnrlgvx7yx4m