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

TL;DR

This paper investigates how quantum chaos manifests in ordered structures through scattering techniques like LEED, showing that complex systems exhibit probability distributions aligned with quantum chaos universality classes.

Contribution

It introduces a theoretical model linking quantum chaos signatures to diffraction intensity distributions in LEED, highlighting the role of multiple scattering and system complexity.

Findings

Probability distributions match the $$ distribution for complex systems.

Quantum chaos signatures are observed in diffraction intensity statistics.

Chaoticity may influence correlation factors like Pendry R-factor.

Abstract

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.