Integrable systems with impurity

TL;DR

This paper discusses how to extend integrable systems to include impurities that can reflect and transmit particles, using RT algebras, overcoming previous limitations on translation-invariant models.

Contribution

It introduces a method to incorporate impurities into integrable systems via RT algebras, enabling reflection and transmission without violating translation invariance.

Findings

RT algebras provide a natural framework for impurity problems

Any integrable system can be adapted to include impurities

The method avoids recent no-go theorems on translation-invariant S-matrices

Abstract

After reviewing some basic properties of RT algebras, which appear to be the natural framework to deal with integrable systems in presence of an impurity, we show how any integrable system (including these possessing translation invariance) can be promoted to an integrable system with an impurity which can reflect and transmit particles. The technics allows bulk translation invariant $S$-matrices while avoiding the no-go theorem stated recently about these laters. Presented at the Vth International workshop on Lie theory and its applications in physics, Varna (Bulgaria), June 16-22, 2003