Statistics of eigenfunctions in 1D tight binding model: Distribution of Riccati variable

For energy eigenfunctions in 1D tight binding model, the distribution of ra tios of the nearest components (Riccati variable), denoted by f(p), gives i nformation on their fluctuation properties. The shape of f(p) is studied nu merically for three versions of the 1D tight binding model. It is shown tha t when perturbation is strong the shape of f(p) is usually quite close to t hat of the Lorentzian distribution and in the case of weak perturbation the shape of the central part of f(p) is model-dependent while the shape of ta ils are still close to the Lorentzian form.