Pumping in quantum dots and non-Abelian matrix Berry phases

We have investigated pumping in quantum dots from the perspective of non-Abelian (matrix) Berry phases by solving the time-dependent Schrodinger equation exactly for adiabatic changes. Our results demonstrate that a pumped charge is related to the presence of a finite matrix Berry phase. When consecutive adiabatic cycles are performed the pumped charge of each cycle is different from that of the previous ones. (C) 2008 Elsevier Ltd. All rights reserved.