  Fragmentation of bosons and pairs in a trapped imbalanced bosonic mixture is
investigated analytically using an exactly solvable model, the generic
harmonic-interaction model for mixtures. Closed-form expressions for the
eigenvalues and eigenfunctions of the reduced one-particle and two-particle
density matrices as a function of all parameters, the masses, numbers of
bosons, and the intraspecies and interspecies interactions, are obtained and
analyzed. As an application, we consider a system made of $N_1=100$
non-interacting species $1$ bosons embedded in a bath made of $N_2=10^6$
non-interacting species $2$ bosons, and show how fragmentation of the system's
bosons and pairs emerges from the system--bath interaction only. Interestingly,
the lighter the bosons comprising the bath are the stronger is the system's
fragmentation. Further applications are briefly discussed.
