Quasiparticle Energy Relaxation in a Gas of One-Dimensional Fermions with Coulomb Interaction.

We consider a system of charged one-dimensional spin-1/2 fermions at low temperature. We study how the energy of a highly excited quasiparticle (or hole) relaxes toward the chemical potential in the regime of weak interactions. The dominant relaxation processes involve collisions with two other fermions. We find a dramatic enhancement of the relaxation rate at low energies, with the rate scaling as the inverse sixth power of the excitation energy. This behavior is caused by the long-range nature of the Coulomb interaction.