From particles to spins: Eulerian formulation of supercooled liquids and glasses

TL;DR

This paper introduces an Eulerian framework for studying supercooled liquids and glasses, enabling better analysis of spatial heterogeneities and connections to spin glass models, demonstrated through colloidal suspension experiments.

Contribution

It proposes a novel Eulerian formulation that links particle and spin systems, facilitating the study of dynamical heterogeneities in supercooled liquids and glasses.

Findings

Eulerian formulation simplifies analysis of spatial heterogeneities.

Framework connects structural and spin glass problems.

Applied to colloidal suspensions near glass transition.

Abstract

The dynamics of supercooled liquid and glassy systems are usually studied within the Lagrangian representation, in which the positions and velocities of distinguishable interacting particles are followed. Within this representation, however, it is difficult to define measures of spatial heterogeneities in the dynamics, as particles move in and out of any one given region within long enough times. It is also non-transparent how to make connections between the structural glass and the spin glass problems within the Lagrangian formulation. We propose an Eulerian formulation of supercooled liquids and glasses that allows for a simple connection between particle and spin systems, and that permits the study of dynamical heterogeneities within a fixed frame of reference similar to the one used for spin glasses. We apply this framework to the study of the dynamics of colloidal particle suspensions for packing fractions corresponding to the supercooled and glassy regimes, which are probed via confocal microscopy.