Dissipationless kinetics of one-dimensional interacting fermions

We study the problem of evolution of a density pulse of one-dimensional interacting fermions with a nonlinear single-particle spectrum. We show that, despite the non-Fermi-liquid nature of the problem, nonequilibrium phenomena can be described in terms of a kinetic equation for certain quasiparticles related to the original fermions by a nonlinear transformation which decouples the left- and right-moving excitations. Employing this approach, we investigate the kinetics of the phase-space distribution of the quasiparticles and thus determine the time evolution of the density pulse. This allows us to explore a crossover from the essentially free-fermion evolution for weak or short-range interaction to hydrodynamics emerging in the case of sufficiently strong, long-range interaction.