 
Summary: ANNALS OF PHYSICS 206, 440493 (1991)
Adiabatic Quantum Transport in Networks
with Macroscopic Components
J. E. AVRON
Department of Physics, Technion, Hafia 32000, Israel
AND
L. SADUN
Courant Institute of Mathematical Sciences, New York University,
New York, New York 10012
Received June 4, 1990
We study the Chern numbers associated with the quantum adiabatic conductances in
networks that have mesoscopic and macroscopic components. The classes of networks
considered have links that are singlemode electron waveguides, with commensurate lengths,
and three independent flux tubes that thread three loops. The mesoscopic part of the networks
have few vertices and the macroscopic parts are made of few long leads or long loops. For
such networks the analysis of the Schrodinger operator reduces to the study of small matrices.
We analyse various classes of such networks qualitatively and solve explicitly a representative
model in each class. We find two scenarios that are the analogs of the integer and classical
Hall effects. In particular, the adiabatic transport at zero temperature for noninteracting
Fermions, is an integer in one scenario and a real (i.e., noninteger) number, in the other. We
