We study a system of interacting electrons on a one-dimensional quantum ring using exact diagonalization and the variational quantum Monte Carlo method. We examine the accuracy of the Slater-Jastrow -type many-body wave function and compare energies and pair distribution functions obtained from the two approaches. Our results show that this wave function captures most correlation effects. We then study the smooth transition to a regime where the electrons localize in the rotating frame, which for the ultrathin quantum ring system happens at quite high electron density.

We introduce quantitative measures for the description of the electric and magnetic coherence in a stationary, random electromagnetic field at two points, in a volume, and in the Fourier space. These quantities are applied to free electromagnetic fields, and several theorems regarding the relationship between the two types of coherences in such fields are established. Fields which are statistically homogeneous, and those which, in addition, are statistically isotropic are considered separately. Furthermore, the connection between the electric and magnetic coherence is exemplified for some specific statistically homogeneous fields.