Title: Kinetics of spin-charge coupled one-dimensional electron liquids

Abstract: The Luttinger liquid model of one-dimensional electron liquids advocates that elementary excitations of the system are charge and spin densities waves. These collective modes do not interact and propagate with different velocities so that the charge and spin of an electron move apart in time. This paradigm of the spin-charge separation is naturally violated once effects of electron band curvature and backscattering are accounted for explicitly within the model. We consider a generic case of spin-1/2 electron liquids in which emerging spin-charge coupling even at zero magnetic field leads to an effective umklapp scattering of spin excitations on thermal plasmons that degrades electric current. This effect ultimately leads to equilibration of the system and temperature dependent correction to conductance of quantum wires. We will also discuss basic scattering processes compatible with the symmetry of the problem and conservation laws that lead to the decay of plasmons into the spin modes. From a closed set of coupled kinetic equations for the spin-charge excitations we solve the problem of thermal conductance of interacting electrons for an arbitrary relation between the quantum wire length and spin-charge thermalization length.