2018/04/18 by Boris A. Malomed, Malomed, Boris A.
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Optics (physics.optics) #Pattern Formation and Solitons (nlin.PS) #Quantum Gases (cond-mat.quant-gas) #Quantum, superfluid, helium dynamics #Spectroscopy and Quantum Chemical Studies #cond-mat.quant-gas #nlin.PS #physics.optics
paper · pdf · doi:10.48550/arxiv.1804.06607
To be published in Condensed Matter (Special Issue "Proceedings of the conference SuperFluctuations 2017")
arxiv created 2018/04/18 · openalex publication_date 2018/04/18 · arxiv updated 2018/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is well known that attractive potential which is inversely proportional to the squared distance from the origin gives rise to the critical quantum collapse in the framework of the three-dimensional (3D) linear Schroedinger equation. This article summarizes theoretical analysis, chiefly published in several original papers, which demonstrates suppression of the collapse caused by this potential, and the creation of the otherwise missing ground state in a 3D gas of bosonic dipoles pulled by the same potential to the central charge, with repulsive contact interactions between them, represented by the cubic term in 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 carrying angular momentum are constructed in the model with the symmetry reduced from spherical to cylindrical by an external polarizing field. Interplay of the collapse suppression and miscibility-immiscibility transition is considered in a binary condensate. The consideration of the 3D setting in the form of the many-body quantum system, with the help of the Monte Carlo method, demonstrates that, although the quantum collapse cannot be fully suppressed, the self-trapped states, predicted by the GPE, exist in the many-body setting as metastable modes protected against the collapse by a tall potential barrier.