Time Scales for transitions between free energy minima of a hard sphere system

TL;DR

This paper introduces a Monte Carlo method to calculate transition times between metastable states in a dense hard sphere system, revealing a sharp increase near a critical density and independence from sample size.

Contribution

A novel Monte Carlo approach for measuring transition times between free energy minima in hard sphere systems, highlighting a critical density where timescales sharply increase.

Findings

Transition times increase with density

Sharp crossover near a critical density

No dependence on sample size

Abstract

Time scales associated with activated transitions between glassy metastable states of a free energy functional appropriate for a dense hard sphere system are calculated by using a new Monte Carlo method for the local density variables. We calculate the time the system,initially placed in a shallow glassy minimum of the free energy, spends in the neighborhood of this minimum before making a transition to the basin of attarction of another free energy minimum. This time scale is found to increase with the average density. We find a crossover density near which this time scale increases very sharply and becomes longer than the longest times accessible in our simulation. This scale shows no evidence of dependence on sample size.