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Mean-Field Theory, Mode-Coupling Theory, and the Onset Temperature in Supercooled Liquids

Yisroel Brumer·David R. Reichman
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Abstract

We consider the relationship between the temperature at which averaged energy landscape properties change sharply ($T_{o}$), and the breakdown of mean-field treatments of the dynamics of supercooled liquids. First, we show that the solution of the wavevector dependent mode-coupling equations undergoes an ergodic-nonergodic transition consistently close to $T_{o}$. Generalizing the landscape concept to include hard-sphere systems, we show that the property of inherent structures that changes near $T_{o}$ is governed more fundamentally by packing and free volume than potential energy. Lastly, we study the finite-size Random Orthogonal Model (ROM), and show that the onset of noticeable corrections to mean-field behavior occurs at $T_{o}$. These results highlight new connections between the energy landscape and mode-coupling approach to supercooled liquids, and identify what features of the relaxation of supercooled liquids are properly captured by mode-coupling theory.

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Yisroel Brumer, David R. Reichman. 2003-06-23. Mean-Field Theory, Mode-Coupling Theory, and the Onset Temperature in Supercooled Liquids. https://doi.org/10.1103/physreve.69.041202

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