EDGE AND BULK TRANSPORT IN VARIABLY CONNECTED QUANTUM HALL CONDUCTOR

We have performed an experiment in the quantum Hall regime using a geo metry that has connectivity between two and three depending on the app lied gate voltage. The measurements may be interpreted in tens of eith er bulk or edge transport. However, the variable connectivity reveals fundamental differences in the current flow through the gated region i n the two pictures. In the edge picture this current does not link the measurement contacts and is dissipationless; in the bulk picture it l inks the contacts and requires dissipation to flow. This extends previ ous results on the equivalence of the two pictures in simply connected geometries.