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An energy-landscape-based crossover temperature in glass-forming liquids

The systematic identification of temperature scales in supercooled liquids that are key to understanding those liquids' underlying glass properties, and the latter's formation-history dependence, is a challenging task. Here we study the statistics of particles' squared displacements $δr^2$ between equilibrium liquid configurations at temperature $T$, and their underlying inherent states, using computer simulations of 11 different computer-glass-formers. We show that the relative fluctuations of $δr^2$ are nonmonotonic in $T$, exhibiting a maximum whose location defines the crossover temperature $T_{\small{\mathsf{X}}}$. Therefore, $T_{\small{\mathsf{X}}}$ marks the point of maximal heterogeneity during the process of tumbling down the energy landscape, starting from an equilibrium liquid state at temperature $T$, down to its underlying inherent state. We extract $T_{\small{\mathsf{X}}}$ for the 11 employed computer glasses, ranging from tetrahedral glasses to packings of soft elastic spheres, and demonstrate its usefulness in putting the elastic properties of different glasses on the same footing. Interestingly, we further show that $T_{\small{\mathsf{X}}}$ marks the crossover between two distinct regimes of the mean $\langleδr^2\rangle$: a high temperature regime in which $\langleδr^2\rangle$ scales approximately as $T^{0.5}$, and a deeply-supercooled regime in which $\langleδr^2\rangle$ scales approximately as $T^{1.3}$. Further research directions are discussed.