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We consider two particles hopping on a chain with a contact interactionbetween them. At strong interaction, there is a molecular bound state separatedby a direct gap from a continuous band of atomic states. Introducing weakdisorder in the interaction, the molecular state becomes Anderson localized. Atstronger disorder, part of the molecular band delocalizes and dissociates dueto its hybridization to the atomic band. We characterize these differentregimes by computing the density of states, the inverse participation ratio,the level-spacing statistics and the survival probability of an initiallylocalized state. The atomic band is best described as that of a rough billiardfor a single particle on a square lattice that shows signatures of quantumchaos. In addition to typical "chaotic states", we find states that arelocalized along only one direction. These "separatrix states" are morelocalized than chaotic states, and similar in this respect to scarred states,but their existence is due to the separatrix iso-energy line in theinteraction-free dispersion relation, rather than to unstable periodic orbits.

Two particles on a chain with disordered interaction: Localization and dissociation of bound states and mapping to chaotic billiards