However, as a major difference to a direct expectation-value approach, both many-body and quantum-optical interactions generate correlations sequentially. In several relevant problems, one indeed has a situation where only the lowest-order clusters are initially nonvanishing while the higher-order clusters build up slowly. In this situation, one can omit the hierarchical coupling, H i [ Δ Δ ⟨ ⟨ C ^ ^ + 1 ⟩ ⟩ ] , at the level exceeding C -particle clusters. As a result, the equations become closed and one only needs to compute the dynamics up to C -particle correlations in order to explain the relevant properties of the system. Since C is typically much smaller than the overall particle number, the cluster-expansion approach yields a pragmatic and systematic solution scheme for many-body and quantum-optics investigations.