An integrable case of the p+ip pairing Hamiltonian interacting with its environment

We consider a generalisation of the p+ip pairing Hamiltonian with external interaction terms. These terms allow for the exchange of particles between the system and its environment. As a result the u(1) symmetry associated with conservation of particle number, present in the p+ip Hamiltonian, is broken. Nonetheless the generalised model is integrable. We establish integrability using the Boundary Quantum Inverse Scattering Method, with one of the reflection matrices chosen to be non-diagonal. We also derive the corresponding Bethe Ansatz Equations, the roots of which parametrise the exact solution for the energy spectrum.