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It is shown that, for a Hamiltonian with a band structure, the half width oflocal spectral density of states, or strength function, is closely related tothe width of the nonperturbative (NPT) parts of energy eigenfunctions. In theWigner-band random-matrix model, making use of a generalized Brillouin-Wignerperturbation theory, we derive analytical expressions for the width of the NPTparts under weak and strong perturbation. An iterative algorithm is given, bywhich the NPT widths can be computed efficiently, and is used in numerical testof the analytical predictions.

Half-width of local spectral density of states given by width of nonperturbative parts of eigenfunctions: The Wigner-band-matrix model