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

Abstract

We study the problem of separation of variables for classical integrable Hamiltonian systems governed by non-skew-symmetric non-dynamical -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.