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It is well known that attractive potential which is inversely proportional tothe squared distance from the origin gives rise to the critical quantumcollapse in the framework of the three-dimensional (3D) linear Schroedingerequation. This article summarizes theoretical analysis, chiefly published inseveral original papers, which demonstrates suppression of the collapse causedby this potential, and the creation of the otherwise missing ground state in a3D gas of bosonic dipoles pulled by the same potential to the central charge,with repulsive contact interactions between them, represented by the cubic termin the respective Gross-Pitaevskii equation (GPE). In two dimensions (2D),quintic self-repulsion is necessary for the suppression of the collapse;alternatively, this may be provided by the effective quartic repulsion,produced by the Lee-Huang-Yang correction to the GPE. 3D states carryingangular momentum are constructed in the model with the symmetry reduced fromspherical to cylindrical by an external polarizing field. Interplay of thecollapse suppression and miscibility-immiscibility transition is considered ina binary condensate. The consideration of the 3D setting in the form of themany-body quantum system, with the help of the Monte Carlo method, demonstratesthat, although the quantum collapse cannot be fully suppressed, theself-trapped states, predicted by the GPE, exist in the many-body setting asmetastable modes protected against the collapse by a tall potential barrier.

Suppression of quantum-mechanical collapse in bosonic gases with intrinsic repulsion: A brief review