One-dimensional interacting electrons beyond the Dzyaloshinskii-Larkin theorem

We consider one-dimensional (1D) interacting electrons beyond the Dzyaloshinskii-Larkin theorem, i.e., keeping forward-scattering interactions among the electrons but adding a nonlinear correction to the electron dispersion relation. The latter generates multiloop corrections to the polarization operator and electron self-energy, thereby providing a variety of inelastic processes affecting equilibrium as well as nonequilibrium properties of the 1D system. We first review the computation of equilibrium properties, e.g., the high-frequency part of the dynamical structure factor and corrections to the electron-electron scattering rate. On this basis, microscopic equilibration processes are identified and a qualitative estimate of the relaxation rate of thermal carriers is given.