Dissipationless kinetics of one-dimensional interacting fermions

Abstract

We study the problem of evolution of a density pulse of one-dimensional\ninteracting fermions with a non-linear single-particle spectrum.\n We show that, despite non-Fermi-liquid nature of the problem, non-equilibrium\nphenomena can be described in terms of a kinetic equation for certain\nquasiparticles related to the original fermions by a non-linear transformation\nwhich decouples the left- and right-moving excitations. Employing this\napproach, we investigate the kinetics of the phase space distribution of the\nquasiparticles and thus determine the time evolution of the density pulse. This\nallows us to explore a crossover from the essentially free-fermion evolution\nfor weak or short-range interaction to hydrodynamics emerging in the case of\nsufficiently strong, long-range interaction.\n