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Updated: Oct 9, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Dynamics of liquids in the large-dimensional limit
Chen Liu1, Giulio Biroli2, David R Reichman3
1Laboratoire de Physique de l'École Normale Supérieure, ENS, Université PSL, Centre National de la Recherche Scientifique, Sorbonne Université, Université de Paris, F-75005 Paris, France and Department of Chemistry, Columbia University, New York, New York 10027, USA.
Abstract:
In this paper 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 insight into the physical features associated with high-dimensional liquids and glass formation. Most importantly, our construction provides a 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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