The dimensional evolution of structure and dynamics in hard sphere liquids

TL;DR

This study explores how the structure and dynamics of hard sphere liquids evolve with increasing dimension, using novel simulation techniques up to 13 dimensions to bridge the gap between finite-dimensional and mean-field theories.

Contribution

The paper introduces a simulation approach that enables studying hard sphere liquids up to 13 dimensions, providing insights into the dimensional evolution of their structure and dynamics.

Findings

Smooth evolution of structure and dynamics with increasing dimension

Identification of features missing in finite-dimension theories

Bridging finite-dimensional and mean-field descriptions

Abstract

The formulation of the mean-field, infinite-dimensional solution of hard sphere glasses is a significant milestone for theoretical physics. How relevant this description might be for understanding low-dimensional glass-forming liquids, however, remains unclear. These liquids indeed exhibit a complex interplay between structure and dynamics, and the importance of this interplay might only slowly diminish as dimension $d$ increases. A careful numerical assessment of the matter has long been hindered by the exponential increase of computational costs with $d$. By revisiting a once common simulation technique involving the use of periodic boundary conditions modeled on $D_d$ lattices, we here partly sidestep this difficulty, thus allowing the study of hard sphere liquids up to $d=13$. Parallel efforts by Mangeat and Zamponi [Phys. Rev. E 93, 012609 (2016)] have expanded the mean-field description of glasses to finite $d$ by leveraging standard liquid-state theory, and thus help bridge the gap from the other direction. The relatively smooth evolution of both structure and dynamics across the $d$ gap allows us to relate the two approaches, and to identify some of the missing features that a finite-$d$ theory of glasses might hope to include to achieve near quantitative agreement.