Equilibrium and non-equilibrium dynamics in random-energy landscapes

Thermally activated transport in rugged energy landscapes is discussed with respect to dispersive transport properties and non-equilibrium ageing phen omena. The disperse transport features are treated by a particular effectiv e-medium approximation that allows one to handle asymmetric hopping rates. This approximation is shown to provide a good account for the approximate s caling properties of conductivity spectra observed in ionic glasses. For th e ageing phenomena we find that the characteristic correlation times can de pend on the waiting time in various ways, including normal ageing and subag eing behaviour, as well as other laws. The possible occurrence of multiple- scaling regimes is demonstrated explicitly.