On the Dynamics of Liquids in the Large-Dimensional Limit

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.

References in corpus (5)

• Theoretical perspective on the glass transition and amorphous materials
• Jamming versus Glass Transitions
• Glass transition of hard spheres in high dimensions
• Active hard-spheres in infinitely many dimensions
• Mean-field caging in a random Lorentz gas

Cited by in corpus (5)

• Local dynamical heterogeneity in glass formers
• Aging by near-extinctions in many-variable interacting populations
• The dimensional evolution of structure and dynamics in hard sphere liquids
• Rigorous dynamical mean field theory for stochastic gradient descent methods
• Gradient descent dynamics and the jamming transition in infinite dimensions