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arXiv · 2108.02378

On the Dynamics of Liquids in the Large-Dimensional Limit

Chen Liu·Giulio Biroli·David Reichman·Grzegorz Szamel
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Abstract

In this work, we analytically derive the exact closed dynamical equations for a liquid with short-ranged interactions in large spatial dimensions using the same statistical mechanics tools employed to analyze Brownian motion. Our derivation greatly simplifies the original path-integral-based route to these equations and provides new insight into the physical features associated with high-dimensional liquids and glass formation. Most importantly, our construction provides a facile route to the exact dynamical analysis of important related dynamical problems, as well as a means to devise cluster generalizations of the exact solution in infinite dimensions. This latter fact opens the door to the construction of increasingly accurate theories of vitrification in three-dimensional liquids.

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Chen Liu, Giulio Biroli, David Reichman, Grzegorz Szamel. 2021-08-05. On the Dynamics of Liquids in the Large-Dimensional Limit. https://doi.org/10.1103/physreve.104.054606

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