1. Dynamics of liquids in the large-dimensional limit
- Author
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Grzegorz Szamel, Giulio Biroli, David R. Reichman, and Chen Liu
- Subjects
Physics ,Exact solutions in general relativity ,0103 physical sciences ,Dynamics (mechanics) ,Cluster (physics) ,Statistical mechanics ,Limit (mathematics) ,Statistical physics ,010306 general physics ,01 natural sciences ,Equations for a falling body ,Brownian motion ,010305 fluids & plasmas - 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.
- Published
- 2021