Dissipationless kinetics of one dimensional interacting fermions

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.

4+ pages, supplementary materials are attached as appendix

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• Relaxation in Luttinger liquids: Bose-Fermi duality
• Equilibration in one-dimensional quantum hydrodynamic systems
• Superluminal moving defects in the Ising spin chain
• Effective mass of elementary excitations in Galilean-invariant integrable models
• Plasmonic shock waves and solitons in a nanoring
• Kinetic Theory for Interacting Luttinger Liquids
• Thermal Transport in One Dimensional Electronic Fluid
• Fate of classical solitons in one-dimensional quantum systems
• Equilibration in a chiral Luttinger liquid
• Pulse propagation in interacting one dimensional Bose liquid
• Anomalous Hydrodynamics in One Dimensional Electronic Fluid
• The fate of quantum shock waves at late times
• Solitons in a one-dimensional Wigner crystal
• Boundary versus bulk behavior of time-dependent correlation functions in one-dimensional quantum systems
• Long lifetimes of ultra-hot particles in interacting Fermi systems
• Quantum fluctuating theory for one-dimensional shock waves
• Charge fractionalization beyond the Luttinger liquid paradigm: an analytical consideration
• From Luttinger liquids to Luttinger droplets via higher-order bosonization identities
• Nonlinear effects on charge fractionalization in critical chains