Statistical Study for Eigenfunctions of 1-dimensional Tight Binding Model

TL;DR

This paper numerically investigates the distribution of ratios of eigenfunction components in 1D tight binding models, revealing Lorentzian-like behavior under strong perturbations and model-dependent features under weak perturbations.

Contribution

It provides a detailed numerical analysis of eigenfunction component ratios in various 1D tight binding models, highlighting their fluctuation properties under different perturbation strengths.

Findings

Strong perturbation leads to Lorentzian distribution of component ratios.

Weak perturbation results in model-dependent central distribution with Lorentzian tails.

Distribution shape varies with perturbation strength and model specifics.

Abstract

For energy eigenfunctions of 1-dimensional tight binding model, the distribution of ratio of their nearest components, denoted by f(p), gives information for their fluctuation properties. The shape of f(p) is studied numerically for three versions of the 1D tight binding model. It is found that when perturbation is strong the shape of f(p) is usually quite close to that of the Lorentzian distribution. In the case of weak perturbation the shape of the central part of f(p) is model-dependent while tails of f(p) are still close to the Lorentzian form.