Charge-conserving equilibration of quantum Hall edge states

We address the experimentally relevant situation, where a nonequilibrium state is created by injecting charge current into a chiral quantum Hall edge state. We show that the commonly accepted picture of the full equilibration of a nonequilibrium state at finite distances contradicts the charge-conservation requirement. We propose and solve the transmission line model that accounts for the local equilibration process and the charge- and energy-conserving dynamics of the collective mode. We find that the correction of the electron distribution function to its eventual equilibrium form scales down slowly as 1/L at long distances L.