ADIABATIC QUANTUM TRANSPORT IN NETWORKS WITH MACROSCOPIC COMPONENTS

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 single-mode electron wave-guides, 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 Schrödinger 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., non-integer) number, in the other. We also discuss an interpretation of the results in terms of the scattering data. This leads to Landauer type formulas for adiabatic transport. © 1991.