  The energy dependence of the relaxation rate of hot electrons due to
interaction with the Fermi sea is studied. We consider 2D and 3D systems,
quasi-1D quantum wires with multiple transverse bands, as well as
single-channel 1D wires. Our analysis includes both spinful and spin-polarized
setups, with short-range and Coulomb interactions. We show that, quite
generally, the relaxation rate is a non-monotonic function of the electron
energy and decays as a power-law at high energies. In other words, ultra-hot
electrons regain their coherence with increasing energy. Such a behavior was
observed in a recent experiment on multi-band quantum wires, J. Reiner et al,
Phys. Rev. X {\bf 7}, 021016 (2017).
