Quantum coherent equilibration in multipoint electron tunneling into a fractional quantum Hall edge

We have found a solution to a model of tunneling between a multichannel Fermi liquid reservoir and an edge of the principal fractional quantum Hall liquid (FQHL) in the strong-coupling limit. The model explicitly takes into account quantum coherence of electrons in different reservoir channels, the fact that makes it important to determine their mutual exchange statistics. Our solution shows that the statistics is in general hyperfermionic, with the phase branches of the statistical factor $-1$ taking different values $\pi \times \mathrm{odd}$ depending on the distance between the points of tunneling from the reservoir channels into the chiral edge. The choice of the statistics determines the saturated current between the edge and reservoir under nonvanishing bias voltage. If the tunneling points are well separated from one another, the outgoing edge is equilibrated with the reservoir as the number of reservoir channels is increased. The equilibration implies that the universal two-terminal conductance of the FQHL is fractionally quantized, in contrast to a one-dimensional Tomonaga-Luttinger liquid wire, where a similar tunneling model predicts unsuppressed free-electron conductance. On the fundamental level, this difference is associated with the absence of time-reversal symmetry at high energies in the FQHL case manifested in the chiral edge propagation.