Quasi-particles in Fractional Quantum Hall Effect Edge Theories

We propose a quasi-particle formulation of effective edge theories for the fractional quantum Hall effect. For the edge of a Laughlin state with filling fraction ν = 1 m , our fundamental quasi-particles are edge electrons of charge −e and edge quasi-holes of charge + e m . These quasi-particles satisfy exclusion statistics in the sense of Haldane. We exploit algebraic properties of edge electrons to derive a kinetic equation for charge transport between a ν = 1 m fractional quantum Hall edge and a normal metal. We also analyze alternative ‘Boltzmann’ equations that are directly based on the exclusion statistics properties of edge quasi-particles. Generalizations to more general filling fractions (Jain series) are briefly discussed.