Z2-graded classical r-matrices and algebraic Bethe ansatz: Applications to integrable models of quantum optics and nuclear physics

We consider quantum integrable models based on the Lie algebra gl(n) and non-skew-symmetric classical r-matrices associated with Z 2-gradings of gl(n) of the following type: , where . Among the considered models are Gaudin-type models with an external magnetic field, used in nuclear physics to produce proton-neutron Bardeen-Cooper-Schrieer-type models, n-level many-mode Jaynes-Cummings-Dicke-type models of quantum optics, matrix generalization of Bose-Hubbard dimers, etc. We diagonalize the constructed models by means of the 'generalized' nested Bethe ansatz.