  In this paper we discuss some aspects of fragmented condensation from a
mathematical perspective. We first propose a simple way of characterizing
finite fragmentation. Then, inspired by recent results of semiclassical
analysis applied to bosonic systems with infinitely many degrees of freedom, we
address the problem of persistence of fragmented condensation. We show that the
latter occurs in interacting systems, in the mean-field regime, and in the
limit of large gap of the one-body Hamiltonian.
