Eigenvectors under a generic perturbation: non-perturbative results from   the random matrix approach
  We consider eigenvectors of the Hamiltonian $H_0$ perturbed by a generic perturbation $V$ modelled by a random matrix from the Gaussian Unitary Ensemble (GUE). Using the supersymmetry approach we derive analytical results for the statistics of the eigenvectors, which are non-perturbative in $V$ and valid for an arbitrary deterministic $H_0$. Further we generalise them to the case of a random $H_0$, focusing, in particular, on the Rosenzweig-Porter model. Our analytical predictions are confirmed by numerical simulations. 
Kevin Truong and Alexander Ossipov
cond-mat.dis-nn cond-mat.stat-mech math-ph math.MP quant-ph