Charge-conserving equilibration of quantum Hall edge states.

We address the problem of the equilibration of quantum Hall (QH) edge states under the additional constraint of charge conservation.This question applies generally to any chiral quasi-one dimensional states, but it naturally arises in the context of resent experiments with quantum Hall systems. This is because QH edge states carry charge excitations with approximately constant speed, and in a typical mesoscopic experiment, to finite distances. Therefore, edge states dynamics must depend on the initial generally non-equilibrium state via boundary condition. Thus even in the case of a strong coupling of edge states to the bath of neutral excitations, their complete equilibration is not possible. In order to investigate the equilibration process under such conditions, we propose the model describing QH edge states a chiral bosonic channel strongly coupled to an array of identical Ohmic contacts with small capacitances. Such model effectively describes a chiral one-dimensional charged channel with dissipation. Asymptotically close to the equilibrium state, the electron distribution function acquires an almost equilibrium form with the universal correction, which is a function of the energy and distance form the injection point, where a non-equilibrium state is created.