Dynamics of liquids in the large-dimensional limit

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.

Figure 1

Illustration of two-particle dynamics and interactions which manifest in $d=\infty$.

Figure 2

Illustration of the real-space meaning of liquid-state cluster dynamical mean-field theory.