Introducing alpha shapes for the analysis of path integral Monte Carlo results

We present a new technique for the visualization and analysis of the results from Monte Carlo simulations based on α-complexes and α-shapes. The specific application presented is the analysis of the quantum-mechanical behavior of hydrogen molecules and helium atoms on a surface at very low temperatures. The technique is an improvement over existing techniques in two respects. First, the approach allows one to visualize the points on a random walk at varying levels of detail and interactively select the level of detail that is most appropriate. Second, using α-shapes one can obtain quantitative measures of spatial properties of the system, such as the boundary length and interior area of clusters, that would be difficult to obtain otherwise