The dimensional evolution of structure and dynamics in hard sphere liquids

Area of Science:

• Theoretical Physics
• Condensed Matter Physics
• Computational Physics

Background:

• The mean-field infinite-dimensional solution for hard sphere glasses is a theoretical milestone.
• Its relevance to low-dimensional glass-forming liquids, where structure-dynamics interplay is crucial, remains uncertain.
• High computational costs have historically limited numerical studies of hard sphere systems in increasing dimensions.

Purpose of the Study:

• To assess the relevance of mean-field theory for low-dimensional hard sphere liquids.
• To investigate the evolution of structure and dynamics as dimensionality increases.
• To bridge the gap between infinite-dimensional theory and finite-dimensional simulations.

Main Methods:

• Revisiting a simulation technique using periodic boundary conditions on Dd lattices.
• Enabling numerical studies of hard sphere liquids up to dimension d = 13.
• Leveraging standard liquid-state theory to expand mean-field descriptions to finite dimensions.

Main Results:

• Successfully simulated hard sphere liquids up to dimension 13, overcoming previous computational barriers.
• Observed a relatively smooth evolution of both structure and dynamics across dimensions.
• Established a connection between mean-field theory and finite-dimensional approaches.

Conclusions:

• The study provides insights into the dimensional dependence of hard sphere glasses.
• It suggests features that finite-dimensional theories need to incorporate for quantitative accuracy.
• This work facilitates a more comprehensive understanding of glass transition phenomena.