G. Braeunlich, G.M. Graf, G. Ortelli
Equivalence of topological and scattering approaches to quantum pumping
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ABSTRACT.  The Schroedinger equation with a potential periodically varying in time 
is used to model adiabatic quantum pumps. The systems considered may be 
either infinitely extended and gapped or finite and connected to gapless 
leads. Correspondingly, two descriptions of the transported charge, one 
relating to a Chern number and the other to a scattering matrix, have been 
available for some time. Here we generalize the first one and establish its equivalence to the second.