  The temperature dependence of the diffusion coefficient of particles is
studied on lattices with disorder. A model is investigated with both trap and
barrier disorder that was introduced before by Limoge and Bocquet (1990 Phys.
Rev. Lett. (65) 60) to explain an Arrhenian temperature-dependence of the
diffusion coefficient in amorphous substances. We have used a generalized
effective-medium approximation (EMA) by introducing weighted transition rates
as inferred from an exact expression for the diffusion coefficient in
one-dimensional disordered chains. Monte Carlo simulations were made to check
the validity of the approximations. Approximate Arrhenian behavior can be
achieved in finite temperature intervals in three- and higher-dimensional
lattices by adjusting the relative strengths of the barrier and trap disorder.
Exact Arrhenian behavior of the diffusion coefficient can only be obtained in
infinite dimensions.
