Theory for Swap Acceleration near the Glass and Jamming Transitions

TL;DR

This paper develops a theoretical framework for understanding how swap algorithms accelerate the glass transition and alter the jamming point, revealing the role of an effective potential governing particle interactions and size changes.

Contribution

It introduces an effective potential approach to explain swap dynamics, predicts lower energy configurations and altered jamming transition, and proposes a new algorithm for creating ultra-stable glasses.

Findings

Swap dynamics are governed by an effective potential incorporating particle sizes.

Stable configurations under swap are at lower energies and temperatures.

Swap significantly alters the jamming transition in polydisperse systems.

Abstract

Swap algorithms can shift the glass transition to lower temperatures, a recent unexplained observation constraining the nature of this phenomenon. Here we show that swap dynamic is governed by an effective potential describing both particle interactions as well as their ability to change size. Requiring its stability is more demanding than for the potential energy alone. This result implies that stable configurations appear at lower energies with swap dynamics, and thus at lower temperatures when the liquid is cooled. \maa{ The magnitude of this effect is proportional to the width of the radii distribution, and decreases with compression for finite-range purely repulsive interaction potentials.} We test these predictions numerically and discuss the implications of these findings for the glass transition.We extend these results to the case of hard spheres where swap is argued to destroy meta-stable states of the free energy coarse-grained on vibrational time scales. Our analysis unravels the soft elastic modes responsible for the speed up swap induces, and allows us to predict the structure and the vibrational properties of glass configurations reachable with swap. In particular for continuously poly-disperse systems we predict the jamming transition to be dramatically altered, as we confirm numerically. A surprising practical outcome of our analysis is new algorithm that generates ultra-stable glasses by simple descent in an appropriate effective potential.