Local thermal energy as a structural indicator in glasses [Physics]
Identifying heterogeneous structures in glasses—such as localized soft spots—and understanding structure–dynamics relations
in these systems remain major scientific challenges. Here, we derive an exact expression for the local thermal energy of interacting
particles (the mean local potential energy change caused by thermal fluctuations) in glassy systems by a systematic low-temperature
expansion. We show that the local thermal energy can attain anomalously large values, inversely related to the degree of softness
of localized structures in a glass, determined by a coupling between internal stresses—an intrinsic signature of glassy frustration—anharmonicity
and low-frequency vibrational modes. These anomalously large values follow a fat-tailed distribution, with a universal exponent
related to the recently observed universal
ω4 density of states of quasilocalized low-frequency vibrational modes. When the spatial thermal energy field—a “softness field”—is
considered, this power law tail manifests itself by highly localized spots, which are significantly softer than their surroundings.
These soft spots are shown to be susceptible to plastic rearrangements under external driving forces, having predictive powers
that surpass those of the normal modes-based approach. These results offer a general, system/model-independent, physical/observable-based
approach to identify structural properties of quiescent glasses and relate them to glassy dynamics.
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