Dimensional study of the dynamical arrest in a random Lorentz gas

TL;DR

This study investigates how the dynamical arrest in the random Lorentz gas varies with dimension, revealing discrepancies with mode-coupling theory and proposing a geometrical upper bound to better understand the transition.

Contribution

It provides a detailed numerical analysis of the dimensional dependence of dynamical arrest in the RLG and relates it to glass transition theories, offering new scaling insights.

Findings

Dynamical arrest thresholds increase with dimension.

Mode-coupling theory predictions worsen as dimension grows.

A geometrical upper bound for the arrest is proposed.

Abstract

The random Lorentz gas is a minimal model for transport in heterogeneous media. Upon increasing the obstacle density, it exhibits a growing subdiffusive transport regime and then a dynamical arrest. Here, we study the dimensional dependence of the dynamical arrest, which can be mapped onto the void percolation transition for Poisson-distributed point obstacles. We numerically determine the arrest in dimensions d=2-6. Comparing the results with standard mode-coupling theory reveals that the dynamical theory prediction grows increasingly worse with $d$. In an effort to clarify the origin of this discrepancy, we relate the dynamical arrest in the RLG to the dynamic glass transition of the infinite-range Mari-Kurchan model glass former. Through a mixed static and dynamical analysis, we then extract an improved dimensional scaling form as well as a geometrical upper bound for the arrest. The results suggest that understanding the asymptotic behavior of the random Lorentz gas may be key to surmounting fundamental difficulties with the mode-coupling theory of glasses.