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Stability of spherically trapped three-dimensional Bose-Einstein condensates against macroscopic fragmentation

We consider spherically trapped Bose gases in three dimensions with contact interactions, and investigate whether the Bose-Einstein condensate at zero temperature is stable against macroscopic fragmentation into a small number of mutually incoherent pieces. Our results are expressed in terms of a dimensionless interaction measure proportional to the Thomas-Fermi parameter. It is shown that while three-dimensional condensates are inherently much more stable against macroscopic fragmentation than their quasi-one- and quasi-two-dimensional counterparts, they fragment at a sufficiently large value of the dimensionless interaction measure, which we determine both fully numerically and semianalytically from a continuum limit of large particle numbers.