Quantum transport of slow charge carriers in quasicrystals and correlated systems

We show that the semiclassical model of conduction breaks down if the mean free path of charge carriers is smaller than a typical extension of their wave function. This situation is realized for sufficiently slow charge carriers and leads to a transition from a metalliclike to an insulatinglike regime when scattering by defects increases. This explains the unconventional conduction properties of quasicrystals and related alloys. The conduction properties of some heavy fermions or polaronic systems, where charge carriers are also slow, present a deep analogy.