Relaxation of weakly interacting electrons in one dimension

Abstract

We consider the problem of relaxation in a one-dimensional system of interacting electrons. In the limit of weak interactions, we calculate the decay rate of a single-electron excitation, accounting for the nonlinear dispersion. The leading processes that determine the relaxation involve scattering of three particles. We elucidate how particular forms of Coulomb interaction, unscreened and screened, lead to different results for the decay rates and identify the dominant scattering processes responsible for relaxation of excitations of different energies. Interestingly, temperatures much smaller than the excitation energy strongly affect the rate. At higher temperatures the quasiparticle relaxes by exciting copropagating electron-hole pairs, whereas at lowest temperatures the relaxation proceeds via excitations of both copropagating and counterpropagating pairs.

5 pages, 2 figures

References in corpus (6)

• Fermi-Luttinger liquid: Spectral function of interacting one-dimensional fermions
• Spectral function of spinless fermions on a one-dimensional lattice
• Three-particle collisions in quantum wires: Corrections to thermopower and conductance
• Energy relaxation and thermalization of hot electrons in quantum wires
• Thermalization of acoustic excitations in a strongly interacting one-dimensional quantum liquid
• Equilibration of a one-dimensional Wigner crystal