Multi-Magnon Scattering in the Ferromagnetic XXX-Model with Inhomogeneities

TL;DR

This paper calculates multi-magnon scattering amplitudes in an inhomogeneous ferromagnetic XXX-model, providing explicit results for two and three particles and proposing a conjecture for general n-particle amplitudes.

Contribution

It introduces explicit calculations of multi-magnon scattering amplitudes in an inhomogeneous XXX-model and proposes a conjecture for the general n-particle case.

Findings

Explicit two-particle scattering amplitudes

Explicit three-particle scattering amplitudes

Proposed conjecture for n-particle amplitudes

Abstract

We determine the transition amplitude for multi-magnon scattering induced through an inhomogeneous distribution of the coupling constant in the ferromagnetic XXX-model. The two and three particle amplitudes are explicitely calculated at small momenta. This suggests a rather plausible conjecture also for a formula of the general n-particle amplitude.