A transmission matrix for a fused pair of integrable defects in the sine-Gordon model

TL;DR

This paper proposes a transmission matrix for soliton scattering with fused integrable defects in the quantum sine-Gordon model, aligning with classical scattering and revealing defect-soliton relationships.

Contribution

It introduces a novel transmission matrix for fused defects, connecting classical scattering insights with quantum soliton interactions in the sine-Gordon model.

Findings

Transmission matrix consistent with classical scattering

Embedding of soliton and breather S-matrices within the transmission matrix

Fused defects can be interpreted as soliton constituents

Abstract

Within the quantum sine-Gordon model a transmission matrix describing the scattering of a soliton with a fused pair of integrable defects is proposed. The result is consistent with the classical picture of scattering and highlights the differences between two defects located at separated points and two defects fused at the same point. Moreover, the analysis reveals how, for certain choices of parameters, both the soliton-soliton and the lightest-breather-soliton S-matrices of the sine-Gordon model are embedded within the transmission matrix, supporting an interpretation in which defects may be regarded as soliton constituents.