Scattering amplitudes in non-Fermi liquid systems

TL;DR

This paper calculates fundamental scattering amplitudes in non-Fermi liquid systems using form-factors and analyticity, providing exact results for quasiparticle reflection, transmission, and electron-edge processes at specific point contacts.

Contribution

It offers the first closed-form expressions for key scattering amplitudes in non-Fermi liquids at special coupling values, advancing theoretical understanding.

Findings

Exact reflection and transmission amplitudes for Laughlin quasiparticles

Closed-form expressions for electron-edge processes

Simplified probabilities for non-Fermi liquid scattering processes

Abstract

By a mix of form-factors and analyticity techniques, we determine some fundamental scattering amplitudes in non-Fermi liquid systems. These include the reflection and transmission amplitudes for Laughlin quasiparticles at a point contact between two g=1/2 Luttinger liquids, and the e->e_{edge} at a point contact between a Fermi liquid and a g=1/3 Luttinger liquid (all liquids chiral or not). These results are obtained in closed form, and give rise to rather simple expressions for the probabilities of the most basic processes of non Fermi liquid physics at these special values of the couplings.