  We compare the properties of transmission across one-dimensional finite
samples which are associated with two types of "quantum diffusion", one related
to a classical chaotic dynamics, the other to a multifractal energy spectrum.
We numerically investigate models exhibiting one or both of these features, and
we find in all cases an inverse power law dependence of the average
transmission on the sample length. Although in all the considered cases the
quadratic spread of wave packets increases linearly (or very close to linearly)
in time for both types of dynamics, a proper Ohmic dependence is always
observed only in the case of quasi-classical diffusion. The analysis of the
statistics of transmission fluctuations in the case of a fractal spectrum
exposes some new features, which mark further differences from ordinary
diffusion, and enforce the conclusion that the two types of transmission are
intrinsically different.
