Long lifetimes of ultra-hot particles in interacting Fermi systems

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).