Nature of Split Hubbard Bands at Low Densities

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We present a numerical scheme for the Hubbard model that throws light on the rather esoteric nature of the Upper and Lower Hubbard bands that have been invoked often in literature. We present a self consistent solution of the ladder diagram equations for the Hubbard model, and show that these provide, at least in the limit of low densities of particles, a vivid picture of the Hubbard split bands. We also address the currently topical problem of decay of the doublon states that are measured in optical trap studies, using the ladder scheme and also by an exact two particle calculation of a relevant Greens function.