2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/176121Using an effective Hamiltonian including the Zeeman and internal interactions, we describe the quantum theory of magnetization dynamics when the spin system evolves non-adiabatically and out of equilibrium. The Lewis-Riesenfeld dynamical invariant method is employed along with the Liouville-von Neumann equation for the density matrix. We derive a dynamical equation for magnetization defined with respect to the density operator with a general form of magnetization damping that involves the non-equilibrium contribution in addition to the Landau-Lifshitz-Gilbert equation. Two special cases of the radiation-spin interaction and the spin-spin exchange interaction are considered. For the radiation-spin interaction, the damping term is shown to be of the Gilbert type, while in the spin-spin exchange interaction case the results depend on a coupled chain of correlation functions.9 pages, revtex4 file, 2 eps-figures; title and abstract changed; minor changes in the body of text; version to appear in Physical Review BOther Condensed MatterHigh Energy Physics - Theorytext