On microscopic theory of spin-S Bose–Einstein condensate in a magnetic field

The ground state and low-lying collective modes of Bose–Einstein condensate (BEC) of atoms with arbitrary spin in a magnetic field is studied using Bogoliubovʹs model for weakly interacting Bose gas. The equation for vectorial order parameter valid at temperature T→0 is derived and its specific solution is found. This solution corresponds to the formation of BEC of atoms with a definite spin projection onto direction of magnetic field. We study the thermodynamic stability of the found ground state and obtain the expressions for low-lying collective modes.