Strong approximation of time evolution operators for a finite system of oscillators with nonlinear coupling

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Abstract
We consider a system in three space dimensions consisting of a finite number of oscillators with a nonlinear interaction. Using projectors on N-particle subspaces of the Fock space, we show that the time evolution operator is strongly approximatable by exponentials of self-adjoint finite-rank operators (finite-dimensional Hermitian matrices), which can easily be calculated in the corresponding eigenrepresentation.