Strong-coupling branching between edges of fractional quantum Hall liquids

We have developed a theory of quasiparticle backscattering in a system of point contacts formed between single-mode edges of several fractional quantum Hall liquids (FQHLs) with different filling factors ν_j and one common single-mode edge ν₀ of another FQHL. In the strong-tunneling limit, the model of quasiparticle backscattering is obtained by the duality transformation of the electron tunneling model. The new physics introduced by the multipoint-contact geometry of the system is coherent splitting of backscattered quasiparticles at the point contacts in the course of propagation along the common edge ν₀. The "branching ratios" characterizing the splitting determine the charge and exchange statistics of the edge quasiparticles that can be different from those of Laughlin's quasiparticles in the bulk of FQHLs. Accounting for the edge statistics is essential for the system of more than one point contact and requires the proper description of the flux attachment to tunneling electrons.