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A kinetic theory for quantum transport in aperiodic media. (English) Zbl 0960.82029

Summary: Transport theory is reinvestigated in a one-particle model including dissipation mechanism 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.

MSC:

82C70 Transport processes in time-dependent statistical mechanics
82D25 Statistical mechanics of crystals
46L60 Applications of selfadjoint operator algebras to physics
58B32 Geometry of quantum groups
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