FRACTAL VERSUS QUASI-CLASSICAL DIFFUSIVE TRANSPORT IN A CLASS OF QUANTUM-SYSTEMS

We compare the properties of transmission across one-dimensional finit e samples which are associated with two types of quantum diffusion, on e 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 incre ases linearly (or very close to linearly) in time for both types of dy namics, a proper Ohmic dependence is always observed only in the case of quasiclassical diffusion. The analysis of the statistics of transmi ssion 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 intrinsi cally different.