Low-density spinor Bose gas of particles with arbitrary spin

The properties of the ground state and the spectrum of elementary excitations of an ultracold rarefied three-dimensional Bose gas of particles with arbitrary nonzero spin are investigated. It is assumed that the bare interaction consists of two parts: a short-range isotropic interaction that is independent of spin orientation and a long-range anisotropic spin-spin interaction of dipole-dipole type. The Gross-Pitaevskii equation is obtained. It is shown using this equation that the renormalized interaction, determined by the contribution of high momenta, plays an important role in the formation of the spin structure of the ground state and the density dependence of the chemical potential. It is established that there exists a range of parameters of the bare-interaction pair potential where the ground state is ferromagnetic. Criteria for the stability of this state are found. An equation describing the dynamics of the spin density is obtained. The spectrum of elementary excitations is determined.