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

TL;DR

This paper establishes a relationship between the local spectral density's half-width and the nonperturbative parts of eigenfunctions in band-structured Hamiltonians, providing analytical and numerical tools for its evaluation.

Contribution

It introduces analytical expressions and an efficient iterative algorithm for calculating the nonperturbative parts' width in Wigner-band matrices, validated through numerical tests.

Findings

Analytical formulas for NPT widths under different perturbation regimes.

An iterative algorithm for efficient NPT width computation.

Numerical validation of theoretical predictions.

Abstract

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