Impurity effects on chiral 1D electron systems
  We studied low energy effects of impurities in several chiral 1D electron systems that contain only excitations moving in one direction. We first considered single-impurity scattering between two branches of 1D chiral Luttinger liquids. The general form of impurity scattering matrix was found which, some times, allow the chemical potentials on the outgoing branches to be higher (or lower) then the maximum (or minimum) chemical potentials on the incoming branches. We also studied the effects of many impurities (with finite density) on two branches of 1D chiral Fermi liquids (that appear on the edge of $\nu=2$ integral quantum Hall liquid). We found that the impurities drive the system to a new fix point at low energies which has an SU(2) symmetry even when the two branches originally have different velocities. (Note a clean system is SU(2) symmetric only when the two branches have the same velocity.) The probability distribution and correlation of scattering matrices at different energies are described by universal functions which are calculated exactly for this new fixed point. 
Xiao-Gang Wen