Quantum chaos on ordered structures by scattering techniques:: Application to low-energy electron diffraction

We analyze statistical probability distributions of intensities collected using diffraction techniques such as low-energy electron diffraction (LEED). A simple theoretical model based an 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 with quantum chaos. A hypothesis on the possible impact of the chaotic nature of wave functions on correlation factors is tested against the behavior of the Pendry R factor and the root mean square deviation factor. [S0163-1829(99)00804-8].