In this talk, we shall discuss how a Schrödinger equation with high dimensionality can be partitioned into weakly interacting subsystems. This type of models describes system-bath type situations where reactive molecular fragments are embedded in a large molecular bath (a protein, or a solvent). We shall consider two schemes of dimension reduction: one based on Taylor expansion (collocation) and the other one based on partial averaging (mean-field or Hartree approximation) for initial data that have a tensor-product structure. We shall also investigate the situation where one of the sets of variables is semi-classically scaled in the coupling variable. In all these cases, we shall motivate the introduction of these schemes, discuss their and we shall show numerical realization. These results are joint works with colleagues from theoretical chemistry, Irene Burghardt and Benjamin Lasorne, and from mathematics, Rémi Carles and Caroline Lasser.

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