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In this paper we investigate the quantum dynamics of two spin-1 systems,$\vec{\textbf{S}}_1$ and $\vec{\textbf{S}}_2$, adopting a generalized$(\vec{\textbf{S}}_1+\vec{\textbf{S}}_2)^2$-nonconserving Heisenberg model. Weshow that, due to its symmetry property, the nine-dimensional dynamics of thetwo qutrits exactly decouples into the direct sum of two sub-dynamics living intwo orthogonal four- and five-dimensional subspaces. Such a reduction isfurther strengthened by our central result consisting in the fact that in thefour-dimensional dynamically invariant subspace, the two qutrits quantumdynamics, with no approximations, is equivalent to that of two non interactingspin 1/2's. The interpretative advantages stemming from such a remarkable andnon-intuitive nesting are systematically exploited and various intriguingfeatures consequently emerging in the dynamics of the two qutrits are deeplyscrutinised. The possibility of exploiting the dynamical reduction brought tolight in this paper for exactly treating as well time-dependent versions of ourHamiltonian model is briefly discussed.

Spin-1/2 sub-dynamics nested in the quantum dynamics of two coupled qutrits