Applications of models of the Gaudin type to condensed matter physics

I will discuss certain quantum models ultimately tracing back to the quasiclassical limits of vertex models. I will demonstrate how the rational and trigonometric Gaudin models with periodic or open boundary conditions allow to study pairing force Hamiltonians (the BCS superconductors are an example) exactly. Also spin-boson systems, useful in various fields like atomic and mesoscopic physics and quantum computations, can be seen as related to Gaudin-like Hamiltonian. Such a relation allow to explore non perturbatively some physical regimes that were proven particularly relevant for the applications.