We investigate theoretically the energy exchange between electrons of two
co-propagating, out-of-equilibrium edge states with opposite spin polarization
in the integer quantum Hall regime. A quantum dot tunnel-coupled to one of the
edge states locally injects electrons at high energy. Thereby a narrow peak in
the energy distribution is created at high energy above the Fermi level. A
second downstream quantum dot performs an energy resolved measurement of the
electronic distribution function. By varying the distance between the two dots,
we are able to follow every step of the energy exchange and relaxation between
the edge states - even analytically under certain conditions. In the absence of
translational invariance along the edge, e.g. due to the presence of disorder,
energy can be exchanged by non-momentum conserving two-particle collisions. For
weakly broken translational invariance, we show that the relaxation is
described by coupled Fokker-Planck equations. From these we find that
relaxation of the injected electrons can be understood statistically as a
generalized drift-diffusion process in energy space for which we determine the
drift-velocity and the dynamical diffusion parameter. Finally, we provide a
physically appealing picture in terms of individual edge state heating as a
result of the relaxation of the injected electrons.Comment: 13 pages plus 6 appendices, 8 figures. Supplemental Material can be
found on http://quantumtheory.physik.unibas.ch/people/nigg/supp_mat.htm
