Laboratoire de Physique Théorique
Toulouse - UMR 5152

We consider the problem of relaxation in a one-dimensional system of interacting particles. 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.

In a system of weakly interacting bosons, the low energy excitation spectrum is determined by the Bogoliubov theory. A single particle excitation, phonon, is not stable and decays due to interactions with other phonons. This mechanism is known as Beliaev damping in higher dimensions. Here we find how phononic excitations decay in one dimension. The leading mechanism is a decay of a single phonon into three others. At zero temperature, a low-energy phonon decays with the rate proportional to seventh power of its momentum. The two problems we consider can not be encountered within the conventional Luttinger liquid theory.