Fragmentation of a trapped bosonic mixture

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 eigenvalues eigenfunctions reduced one-particle two-particle density matrices as function all parameters, masses, numbers bosons, intraspecies interspecies interactions, are obtained analyzed. As application, we consider system made $N_1=100$ non-interacting species $1$ embedded bath $N_2=10^6$ $2$ show how fragmentation system's emerges from system--bath interaction only. Interestingly, lighter comprising stronger fragmentation. Further applications briefly discussed.