Persistent edge current in the fractional quantum Hall effect

We study the persistent edge current in the fractional quantum Hall effect. We give the grand partition functions for edge excitations of hierarchical states coupled to an Aharanov-Bohm flux and derive the exact formula of th e persistent edge current. Any mth hierarchical state, with m > 1, exhibits anomalous oscillations in its flux dependence at low temperatures. The cur rent as a function of the flux converges to the sawtooth function with peri od phi(o) = hc/e at zero temperature. This phenomenon provides a new eviden ce for exotic condensation in the fractional quantum Hall effect. We propos e experiments to measure the persistent edge current and thus to verify the existence of the hierarchy.