Pair functions computed recursively in ordered and disordered lattices

Abstract

In this article I study pairing of two interacting particles in ideal 1D, 2D and Bethe lattices. I employ the method of recursion that has been formulated recently by Berciu et. al. to compute the pair functions in real space without performing any integrations. Although, in higher dimensions the system sizes that can be addressed with this method become limited, for disordered systems this size limit can be increased by employing approximations.