QUANTUM TRANSPORT AND THE EDGE MODES IN THE HIERARCHY FRACTIONAL QUANTUM HALL LIQUID

Quantum transport phenomena in the edge and bulb of the hierarchy frac tional quantum Hall liquid is discussed by constructing an effective C hern-Simons theory for the Abelian quantum Hall states with the detail ed analysis of the boundary condition at the edge. It is found that th e chemical potentials of the gauge fields at the edge are equal to eac h other, and the Hall conductance is always quantized irrespective of the detailed dynamics or the randomness at the edge.