The dimensional evolution of structure and dynamics in hard sphere liquids
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.
Type
Journal articlePermalink
https://hdl.handle.net/10161/24974Collections
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Show full item recordScholars@Duke
Patrick Charbonneau
Professor of Chemistry
Professor Charbonneau studies soft matter. His work combines theory and simulation
to understand the glass problem, protein crystallization, microphase formation, and colloidal
assembly in external fields.

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