Infrared catastrophe in two-quasiparticle collision integral

TL;DR

This paper investigates how small-energy spin-flip scattering processes can cause divergence in the collision integral for non-equilibrium electron distributions in disordered wires, highlighting the need for non-perturbative treatment.

Contribution

It demonstrates the infrared divergence in the collision integral due to spin-flip processes with small energy transfer in a spin-dependent electron distribution.

Findings

Divergence occurs only for M=0 spin magnetization.

The divergence appears in quasi-1D wires with triplet interaction.

Non-perturbative methods are required to regularize the divergence.

Abstract

Relaxation of a non-equilibrium state in a disordered metal with a spin-dependent electron energy distribution is considered. The collision integral due to the electron-electron interaction is computed within the approximation of a two-quasiparticle scattering. We show that the spin-flip scattering processes with a small energy transfer may lead to the divergence of the collision integral for a quasi one-dimensional wire. This divergence is present only for a spin-dependent electron energy distribution which corresponds to the total electron spin magnetization M=0 and only for non-zero interaction in the triplet channel. In this case a non-perturbative treatment of the electron-electron interaction is needed to provide an effective infrared cut-off.