Comparing conductance quantization in quantum wires and Quantum Hall systems

摘要

We propose a new calculation of the DC conductance of a 1-dimensionalelectron system described by the Luttinger model. Our approach is based on theideas of Landauer and B\"{u}ttiker and on the methods of current algebra. Weanalyse in detail the way in which the system can be coupled to externalreservoirs. This determines whether the conductance is renormalized or not. Weshow that although a quantum wire and a Fractional Quantum Hall system aredescribed by the same effective theory, their coupling to external reservoirsis different. As a consequence, the conductance in the wire is quantized ininteger units of $e^2/h$ per spin orientation whereas the Hall conductanceallows for fractional quantization.