Journal
PHYSICAL REVIEW E
Volume 104, Issue 5, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.104.054606
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Funding
- Simons Collaboration Cracking the glass problem [454935, 454951]
- NSF [CHE 1800282]
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This paper analytically derives the exact closed dynamical equations for liquids with short-ranged interactions in large spatial dimensions using statistical mechanics tools. It simplifies the path-integral-based route to these equations and provides insight into high-dimensional liquids and glass formation. The construction also offers a means to analyze related dynamical problems accurately and devise cluster generalizations of the exact solution in infinite dimensions, opening the door to constructing increasingly accurate theories of vitrification in three-dimensional liquids.
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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