Gianluca Panati, Christof Sparber, Stefan Teufel
Geometric currents in piezoelectricity
(125K, AMS-TeX)

ABSTRACT.  As a simple model for piezoelectricity we consider a gas of infinitely many non-interacting electrons subject to a slowly time-dependent periodic potential. We show that in the adiabatic limit the macroscopic current is determined by the geometry of the Bloch bundle. As a consequence we obtain the King-Smith and Vanderbilt formula up to errors smaller than any power of the adiabatic parameter.