Saddles in the Energy Landscape Probed by Supercooled Liquids

We numerically investigate the supercooled dynamics of two simple model liquids exploiting the partition of the multidimensional configuration space in basins of attraction of the stationary points (inherent saddles) of the potential energy surface. We find that the inherent saddle order and potential energy are well-defined functions of the temperature $T$. Moreover, by decreasing $T$, the saddle order vanishes at the same temperature $\left(T_{\mathrm{MCT}}\right)$ where the inverse diffusivity appears to diverge as a power law. This allows a topological interpretation of $T_{\mathrm{MCT}}$: it marks the transition from a dynamics between basins of saddles $(T>\mathrm{}{T}_{\mathrm{MCT}})$ to a dynamics between basins of minima $(T<\mathrm{}{T}_{\mathrm{MCT}})$.