Coupling integrable field theories to mechanical systems at the boundary

@article{Baseilhac2001CouplingIF,
  title={Coupling integrable field theories to mechanical systems at the boundary},
  author={Pascal Baseilhac and Gustav W. Delius},
  journal={Journal of Physics A},
  year={2001},
  volume={34},
  pages={8259-8270}
}
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. 
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References

SHOWING 1-10 OF 33 REFERENCES

New solutions to the reflection equation and the projecting method

New integrable boundary conditions for integrable quantum systems can be constructed by tuning of scattering phases due to reflection at a boundary and an adjacent impurity and subsequent projection…

Boundary conditions for integrable quantum systems

A new class of boundary conditions is described for quantum systems integrable by means of the quantum inverse scattering (R-matrix) method. The method proposed allows the author to treat open…

Boundary S matrix and boundary state in two-dimensional integrable quantum field theory

We study integrals of motion and factorizable S matrices in two-dimensional integrable field theory with boundary. We propose the "boundary cross-unitarity equation," which is the boundary analog of…

Hamiltonian methods in the theory of solitons

The Nonlinear Schrodinger Equation (NS Model).- Zero Curvature Representation.- The Riemann Problem.- The Hamiltonian Formulation.- General Theory of Integrable Evolution Equations.- Basic Examples…

Integrable boundary conditions for classical sine-Gordon theory

The possible boundary conditions consistent with the integrability of the classical sine-Gordon equation are studied. A boundary value problem on the half-line x<or=0 with local boundary condition at…

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

Exact quantization of the sinh-Gordon model

Graded reflection equation algebras and integrable Kondo impurities in the one-dimensional t-J model

Boundary conditions for integrable equations

The problem of constructing boundary conditions for nonlinear equations compatible with higher symmetries is considered. In particular, this problem is discussed for the sine - Gordon, Jiber -…

ON NON-EQUILIBRIUM STATES IN QFT MODEL WITH BOUNDARY INTERACTION