A Kinetic Theory for Quantum Transport in Aperiodic Media

Transport theory is reinvestigated in a one-particle model including dissipation mechanisms through a phenomenological time-dependent part. Using the description of an aperiodic crystal in terms of noncommutative geometry, it is then possible to rigorously derive Kubo formulas for the electric conductivity. Within the framework of the relaxation time approximation, a fractal analysis applied to the spectral measures entering in the Kubo formula allows us to examine anomalous transport owing to quantum interferences. This leads to anomalies in Drude's formula.