40 50 47 v 1 1 7 M ay 2 00 4 On the exactly - solvable pairing models for bosons

On the exactly-solvable pairing models for bosons. Abstract We discuss the construction of the exactly solvable pairing models for bosons in the framework of the Quantum Inverse Scattering method. It is stressed that this class of models is naturally appears in the quasiclassical limit of the algebraic Bethe ansatz transfer matrix. It is pointed out that the new class of the pairing models can be obtained from the fundamental transfer-matrix. Using the electrostatic analogy we reexamine the solution of the pairing model for the case of repulsion. The solution in the weak coupling regime is presented. We propose the new exactly solvable model corresponding to the attractive pairing interaction. The solution of this model in thermodynamic limit is presented. The transition from the superfluid phase with the Bose condensate and the Bogoliubov-type spectrum of excitations in the weak coupling regime to the incompressible phase with the gap in the excitation spectrum in the strong coupling regime is observed.