Doorway states and the Bose-Hubbard model

We apply the doorway method to solve the problem of N bosons in an optical lattice. This method allows for the inclusion of many-body correlations in a dynamically motivated hierarchical way, yielding useful approximations even within subspaces of the full Hilbert space of greatly reduced dimensionality. We calculate some important experimental observables. Excellent qualitative agreement with exact numerical calculations and recent experimental observations is obtained.