Nonequilibrium kinetics of a disordered Luttinger liquid

We develop a kinetic theory for strongly correlated disordered one-dimensional electron systems out of equilibrium, within the Luttinger liquid model. In the absence of inhomogeneities, the model exhibits no relaxation to equilibrium. We derive kinetic equations for electron and plasmon distribution functions in the presence of impurities and calculate the equilibration rate $\gamma_E$. Remarkably, for not too low temperature and bias voltage, $\gamma_E$ is given by the elastic backscattering rate, independent of the strength of electron-electron interaction, temperature, and bias.