 
Summary: Geometry, statistics, and asymptotics of quantum pumps
J. E. Avron,1
A. Elgart,1
G. M. Graf,2
and L. Sadun1,3
1
Department of Physics, Technion, 32000 Haifa, Israel
2
Theoretische Physik, ETHHo¨nggerberg, 8093 Zu¨rich, Switzerland
3
Department of Mathematics, University of Texas, Austin, Texas 78712
Received 16 August 2000
We give a pedestrian derivation of a formula of Bu¨ttiker, Pretre, and Thomas Z. Phys. B 94, 133 1994
BPT relating the adiabatically pumped current to the Smatrix and its time derivatives. We relate the charge
in BPT to Berry's phase and the corresponding Brouwer pumping formula to curvature. As applications we
derive explicit formulas for the joint probability density of pumping and conductance when the Smatrix is
uniformly distributed; and derive a formula that describes hard pumping when the Smatrix is periodic in the
driving parameters.
Brouwer3
and Shutenko et al.,4
