Dissipationless kinetics of one dimensional interacting fermions

TL;DR

This paper investigates the non-equilibrium evolution of density pulses in one-dimensional interacting fermions with non-linear spectra, revealing a crossover from free-fermion behavior to hydrodynamics based on interaction strength.

Contribution

It introduces a kinetic equation framework for quasiparticles that decouples left- and right-movers, enabling analysis of non-Fermi-liquid dynamics in 1D fermion systems.

Findings

Identifies a kinetic description for quasiparticles in non-linear spectra.

Shows a transition from free-fermion to hydrodynamic behavior with increasing interaction.

Provides insights into non-equilibrium dynamics of 1D fermion systems.

Abstract

We study the problem of evolution of a density pulse of one-dimensional interacting fermions with a non-linear single-particle spectrum. We show that, despite non-Fermi-liquid nature of the problem, non-equilibrium phenomena can be described in terms of a kinetic equation for certain quasiparticles related to the original fermions by a non-linear 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.