Manifestation of quantum chaos on ordered structures by scattering techniques: application to Low-Energy Electron Diffraction

We analyze statistical probability distributions of intensities collected by diffraction techniques like Low-Energy Electron Diffraction. A simple theoretical model based in hard-sphere potentials and LEED formalism is investigated for different values of relevant parameters: energy, angle of incidence, muffin-tin potential radius, maximum spherical component $l_{max}$, number of stacked layers, and full multiple-scattering or kinematic model. Given a complex enough system (e.g., including multiple scattering by at least two Bravais lattices), the computed probability distributions agree rather well with a ${\chi }_2^2$ one, characteristic of the Gaussian Unitary Ensemble universality class associated to quantum chaos. A hypothesis on the possible impact of the chaoticity of wavefunctions on correlation factors is tested against the behaviour of the Pendry R-factor and the Root Mean Squared Deviation factor.