Bart De Raedt

Computer simulation of muonium in water

The structure of water molecules surrounding an isolated hydrogen atom (H) or muonium (Mu) is investigated using computer simulation. The water solvent is treated using classical mechanics and a simple effective two body potential that is designed to yield a reasonable solvent structure. Feynman’s path integral approach is used to treat the single quantum impurity (H or Mu). Both the H and Mu atoms are found to be clathrated with average coordination numbers of 18 and 23 water molecules, respectively. The value for the H atom differs little from the results of a purely classical calculation. It is suggested that the lack of isotope effect in certain diffusion controlled reactions of H and Mu is due to the enclathration of  both species.

Monte Carlo Study of the Two-Dimensional Spin-1/2 XY Model

The generalized Trotter formula is used to map the two-dimensional spin-1/2 XY model onto a three-dimensional Ising model with complicated many-spin interactions. This relationship is used to construct an efficient Monte Carlo algorithm. Simulation data for the specific heat and vortex correlation functions give strong evidence for the existence of a phase transition.

Langevin model of the rotational motion of molecules: Two‐dimensional rotator in a cubic potential

The rotational motion of a linear molecule in a potential of cubic symmetry is treated in the framework of the Langevin equation. The corresponding Langevin equation is solved numerically. From these numerical data, time‐dependent correlation functions are extracted and compared with the results of other models. It is found that the harmonic approximation is good for potential barriers higher than about eight times the thermal energy. Earlier models describe the static behavior very well, but they do not describe dynamic properties correctly. For potential barriers comparable to the thermal energy, the Langevin equation seems to provide the most realistic description.

Librational and relaxational motion of molecular impurities in crystals

The dynamics of a single impurity with rotational degrees of freedom in the static crystal field of the host lattice is revisited. We use numerical simulation techniques to calculate the time-dependent correlation functions accurately up to very long times. Then we carry out a spectral analysis of these results, thus obtaining good estimates for the contribution of different representations to the incoherent scattering cross-sections. For some representations we find non-ergodic behaviour, giving rise to delta-function contributions at zero frequency. In the real crystal these contributions will be broadened because the rotator is coupled dynamically to the phonons of the host crystal, which is not taken into account in our simple model.