Recent computational methods permit the determination of the low energ
y states of fair sized systems of localized interacting particles in r
andom media. Making use of such methods, this paper evaluates the natu
re of the low-energy excitations of the system, and it's implications
on conductivity and on ergodicity. Two- and three-dimensional systems
are examined. it is found that the low energy excitations exhibit stro
ng correlation effects, indicating that one-particle theories for equi
librium and non-equilibrium properties are not justified. Ergodicity i
s tested by relaxation at zero temperature. It is found that relaxatio
n time can be extremely long, indicating that the system is not ergodi
c at low temperatures.