Properties of ideal Gaussian glass-forming systems

We introduce the ideal Gaussian glass-forming system as a model to describe the thermodynamics and dynamics of supercooled liquids on a local scale in terms of the properties of the potential energy landscape (PEL). The first ingredient is the Gaussian distribution of inherent structures, the second a specific relation between energy and mobility. This model is compatible with general considerations as well as with several computer simulations on atomic computer glass formers. Important observables such as diffusion constants, structural relaxation times, and kinetic as well as thermodynamic fragilities can be calculated analytically. In this way it becomes possible to identify a relevant PEL parameter determining the kinetic fragility. Several experimental observations can be reproduced. The remaining discrepancies in the experiment can be qualitatively traced back to the difference between small and large systems.