  We study the effect of disorder on the particle density evolution in a
classical Hamiltonian driven lattice setup. If the disorder is localized within
a finite sub-domain of the lattice, the emergence of strong tails in the
density distribution which even increases towards larger positions is shown,
thus yielding a highly non Gaussian particle density evolution. As the key
underlying mechanism we identify the conversion between different components of
the unperturbed systems mixed phase space which is induced by the disorder.
Based on the introduction of individual conversion rates between chaotic and
regular components, a theoretical model is developed which correctly predicts
the scaling of the particle density. The effect of disorder on the transport
properties is studied where a significant enhancement of the transport for
cases of localized disorder is shown, thereby contrasting strongly the merely
weak modification of transport for global disorder.
