Quantum Conductance in Networks

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Abstract
We consider the quantum transport in networks. Arguments similar to those for the quantum Hall effect show that the averaged transport coefficients are quantized. Numerical calculations for a three-loop network yield the values 0, 1, and - 1, depending on the fluxes threading the loops and the quantum state of the net. We characterize the conductance properties of such networks. We also discuss general properties of the transport coefficients in general multiloop networks.