Some rigorous aspects of fragmented condensation

In this paper we discuss some aspects of fragmented condensation from a mathematical perspective. Inspired by techniques of pseudodifferential calculus and semiclassical analysis in Bosonic Quantum Field Theory, we propose a simple way of identifying fragmentation, and we analyze the effects of pair interaction on finite fragmented states. In particular, we focus on the persistence of finite fragmented condensation when the gap between the degenerate ground state and the excited states of the corresponding non-interacting system is very large.