GeoVis: from Geodesics to Viscous liquids

When a liquid is cooled, the text-book prediction is that it crystallizes. However, in many cases crystallization is avoided and the liquid becomes supercooled. Upon further cooling relaxation times and viscosity increase by many orders of magnitude, and eventually the liquid falls out of equilibrium and forms a glass.

Nobel laureate P. W. Anderson stated that understanding the ultra viscous liquid state and its transition to a glass is one of the deepest unsolved problems in solid state physics. Preliminary results suggests that the answer might lie hidden in the realm of mathematics - in particular in the properties of geodesic flows on the high-dimensional surface defined by the potential energy - as a function of all particle coordinates - being constant. The aim of this project is to explore this possibility - if successful it opens up a completely new approach to understanding the dynamics of viscous liquids, as well as the physical aging of glassy materials.