Coupling integrable field theories to mechanical systems at the boundary

TL;DR

This paper introduces an integrable Hamiltonian coupling the sinh-Gordon field theory on a half-line with a boundary oscillator, using Sklyanin's formalism, and extends the method to other integrable models and quantum solutions.

Contribution

It presents a novel integrable boundary coupling of sinh-Gordon theory with a dynamical boundary system and generalizes the approach for other models and quantum cases.

Findings

Constructed an integrable Hamiltonian for sinh-Gordon with boundary oscillator

Applied Sklyanin's formalism to dynamical reflection matrices

Derived the quantum reflection equation solution for the model

Abstract

We present an integrable Hamiltonian which describes the sinh-Gordon model on the half line coupled to a non-linear oscillator at the boundary. We explain how we apply Sklyanin's formalism to a dynamical reflection matrix to obtain this model. This method can be applied to couple other integrable field theories to dynamical systems at the boundary. We also show how to find the dynamical solution of the quantum reflection equation corresponding to our particular example.