Perturbative and nonperturbative parts of eigenstates and local spectral density of states: The Wigner-band random-matrix model

The Wigner-band random-matrix model is studied by making use of a generalization of Brillouin-Wigner perturbation theory. Energy eigenfunctions are shown to be divided into perturbative and nonperturbative parts. Several perturbation strengths predicted by the perturbation theory are found to pray important roles in the variation of the shape of the local spectral density of states with perturbation strength.