Coupling integrable field theories to mechanical systems at the boundary

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.

16 pages

References in corpus (2)

• The boundary supersymmetric sine-Gordon model revisited
• The spectrum of boundary states in sine-Gordon model with integrable boundary conditions

Cited by in corpus (19)

• Deformed Dolan-Grady relations in quantum integrable models
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• Sine-Gordon quantum field theory on the half-line with quantum boundary degrees of freedom
• Hecke algebraic approach to the reflection equation for spin chains
• On $A_{n-1}^{(1)},B_n^{(1)},C_n^{(1)},D_n^{(1)},A_{2n}^{(2)},A_{2n-1}^{(2)}$ and $D_{n+1}^{(2)}$ Reflection $K$-Matrices
• A new class of integrable defects
• Aspects of sine-Gordon solitons, defects and gates
• The generalized non-linear Schrodinger model on the interval
• Integrable boundary conditions and modified Lax equations
• Folding defect affine Toda field theories
• From Hamiltonian to zero curvature formulation for classical integrable boundary conditions
• Generalized q-Onsager algebras and boundary affine Toda field theories
• $A_n^{(1)}$ affine Toda field theories with integrable boundary conditions revisited
• Generalized q-Onsager Algebras and Dynamical K-matrices
• The Massive Klein-Gordon Field Coupled to a Harmonic Oscillator at the Boundary
• N=2 boundary supersymmetry in integrable models and perturbed boundary conformal field theory
• Infinite dimension reflection matrices in the sine-Gordon model with a boundary
• Integrable models with boundaries and defects
• Integrability of the N=2 boundary sine-Gordon model