Separation of variables in anisotropic models: anisotropic Rabi and elliptic Gaudin model in an external magnetic field

Source abstract

Abstract We study the problem of separation of variables for classical integrable Hamiltonian systems governed by non-skew-symmetric non-dynamical s o ( 3 ) ⊗ s o ( 3 ) -valued elliptic r -matrices with spectral parameters. We consider several examples of such models, and perform separation of variables for classical anisotropic one- and two-spin Gaudin-type models in an external magnetic field, and for Jaynes–Cummings–Dicke-type models without the rotating wave approximation.