We investigate energy transfer between counter-propagating quantum Hall edge channels (ECs) in a two-dimensional electron system at filling factor u=1. The ECs are separated by a thin impenetrable potential barrier and Coulomb coupled, thereby constituting a quasi one-dimensional analogue of a spinless Luttinger liquid (LL). We drive one, say hot, EC far from thermal equilibrium and measure the energy transfer rate P into the second, cold, EC using a quantum point contact as a bolometer. The dependence of P on the drive bias indicates breakdown of the momentum conservation, whereas P is almost independent on the length of the region where the ECs interact. Interpreting our results in terms of plasmons (collective density excitations), we find that the energy transfer between the ECs occurs via plasmon backscattering at the boundaries of the LL. The backscattering probability is determined by the LL interaction parameter and can be tuned by changing the width of the electrostatic potential barrier between the ECs.
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