# Trapping Collapse. (arXiv:1802.00846v1 [cond-mat.quant-gas])

Weak potential wells (or traps) in one and two dimensions, and the potential

wells slightly deeper than the critical ones in three dimensions, feature

shallow bound states with localization length much larger than the well radii.

We address a simple fundamental question of how many repulsively interacting

bosons can be localized by such traps. We find that under rather generic

conditions, for both weakly and strongly repulsive particles, in two and three

dimensions--but not in one-dimension!--the potential well can trap infinitely

many bosons. For example, even hard-core repulsive interactions do not prevent

this "trapping collapse" phenomenon from taking place. For the weakly

interacting/dilute regime, the effect can be revealed by the mean-field

argument, while in the case of strong correlations the evidence comes from

path-integral simulations. We also discuss the possibility of having a

transition between the infinite and finite number of trapped particles when

strong repulsive inter-particle correlations are increased.