Hopping in Disordered Media: A Model Glass Former and A Hopping Model

TL;DR

This paper investigates particle hopping in disordered media through two models: a molecular dynamics simulation of a glass-forming liquid revealing cooperative particle motion at low temperatures, and a lattice hopping model analyzed with a novel VAC method.

Contribution

It introduces a new velocity auto-correlation method for analyzing hopping models and provides numerical evidence supporting the cooperative string-like particle motion in a model glass former.

Findings

Hopping dynamics show a secondary displacement peak at low temperatures.

The VAC method accurately computes diffusion in finite disordered systems.

The DCA approximation aligns well with numerical results in the hopping model.

Abstract

Two models involving particles moving by ``hopping'' in disordered media are investigated: I) A model glass-forming liquid is investigated by molecular dynamics under (pseudo-) equilibrium conditions. ``Standard'' results such as mean square displacements, intermediate scattering functions, etc. are reported. At low temperatures hopping is present in the system as indicated by a secondary peak in the distribution of particle displacements during a time interval 't'. The dynamics of the model is analyzed in terms of its potential energy landscape (potential energy as function of the 3N particle coordinates), and we present direct numerical evidence for a 30 years old picture of the dynamics at sufficiently low temperatures. Transitions between local potential energy minima in configuration space are found to involve particles moving in a cooperative string-like manner. II) In the symmetric hopping model particles are moving on a lattice by doing thermally activated hopping over energy barriers connecting nearest neighbor sites. This model is analyzed in the extreme disorder limit (i.e. low temperatures) using the Velocity Auto Correlation (VAC) method. The VAC method is developed in this thesis and has the advantage over previous methods, that it can calculate a diffusive regime in finite samples using periodic boundary conditions. Numerical results using the VAC method are compared to three analytical approximations, including the Diffusion Cluster Approximation (DCA), which is found to give excellent agrement with the numerical results.