On the Dynamics of Liquids in the Large-Dimensional Limit

TL;DR

This paper derives exact dynamical equations for high-dimensional liquids with short-range interactions, simplifying previous methods and offering new insights into glass formation and potential improvements for three-dimensional theories.

Contribution

It provides a simplified, exact derivation of liquid dynamics in large dimensions, enabling advanced analysis and cluster generalizations for better understanding of vitrification.

Findings

Exact dynamical equations for large-dimensional liquids derived

Simplified analytical approach compared to path-integral methods

Framework for developing improved theories of glass formation

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.