Unitary symmetry and generalization of Landau–Lifshitz equation for high spin magnets

The dynamics of magnets with arbitrary spin is described. The relations between the pure and mixed quantum states with magnetic degrees of freedom are considered. Nonlinear dynamic equations of normal and degenerate nonequilibrium states of high spin magnets are obtained. We have analyzed in detail the subalgebras of the Poisson brackets of magnetic values for the cases of magnets with spin s = 1/2, 1, 3/2, possessing the properties of SO(3), SU(3), SU(4), SU(2) × SU(2), SO(4), SO(5) symmetry of the exchange interaction. An explicit form of the polarization density matrix for the spin s = 1 and s = 3/2 magnets in pure quantum states is derived and a range of permitted values of the magnetic degrees of freedom for mixed states is found.

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