Theory of the Quantized Adiabatic Particle Transport

A localized formulation is presented for the quantized adiabatic particle transport (APT) induced by a slow and cyclic potential variation. Finite size effects are studied for the ring geometry and a realistic geometry. The localized description of APT is shown to be equivalent to the Laughlin's gauge invariant argument for the quantum Hall effect. The effect of quantum fluctuation and the possibility of fractionally quantized APT are also discussed.