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.Comment: Ph.D. thesis, 101 pages, 52 figure
