Abstract:  Ergodic many-body systems are expected to reach quasi-thermal equilibrium. Indeed, the energy distribution in quantum Hall edge modes with short-range interactions generally relaxes to a near-thermal asymptotic state that can be described in terms of charge fractionalization. Surprisingly, high-energy electrons injected into a single edge mode with finite range interactions can stabilize over a long time scale in a state far from a thermal one: the resulting many-body state consists of rapidly decaying transient components followed by a near-steady-state distribution with a peak near the injection energy.