Quasiparticle energy relaxation in a gas of one-dimensional fermions with Coulomb interaction

TL;DR

This paper investigates how highly-excited quasiparticles in a one-dimensional Coulomb-interacting fermion gas relax energy, revealing a significant enhancement of relaxation rates at low energies due to long-range interactions.

Contribution

It provides a theoretical analysis of quasiparticle energy relaxation in 1D fermions with Coulomb interactions, highlighting the energy dependence of relaxation rates.

Findings

Relaxation rate scales as inverse sixth power of excitation energy.

Long-range Coulomb interaction causes enhanced low-energy relaxation.

Dominant processes involve three-fermion collisions.

Abstract

We consider a system of charged one-dimensional spin-$\frac{1}{2}$ fermions at low temperature. We study how the energy of a highly-excited quasiparticle (or hole) relaxes toward the chemical potential in the regime of weak interactions. The dominant relaxation processes involve collisions with two other fermions. We find a dramatic enhancement of the relaxation rate at low energies, with the rate scaling as the inverse sixth power of the excitation energy. This behavior is caused by the long-range nature of the Coulomb interaction.