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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 non-linear correction to the electron dispersion relation. The latter generates multi-loop corrections to the polarization operator and electron self-energy thereby providing a variety of inelastic processes affecting equilibrium as well as non-equilibrium 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.