We develop a kinetic theory for strongly correlated one-dimensional electron systems out of equilibrium, within the framework of the Luttinger liquid model. In the absence of disorder (backscattering off impurities), the model is completely integrable and as such exhibits no relaxation to equilibrium. We formulate a theoretical framework to study relaxation processes due to the interplay of disorder and electron-electron interactions, based on kinetic equations for electron and plasmon distribution functions. We calculate the rate of energy relaxation (equilibration) in a disordered Luttinger liquid, relevant to the transport properties of quantum wires at finite bias voltage. Remarkably, for not too low temperature and bias, the energy-relaxation rate is found to be given by the rate of elastic scattering off disorder, independent of the strength of electron-electron interaction and temperature.
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