2023/11/11 by Hidetsugu Sakaguchi, Boris A. Malomed, Sakaguchi, Hidetsugu +1
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Optical properties and cooling technologies in crystalline materials #Pattern Formation and Solitons (nlin.PS) #Quantum Gases (cond-mat.quant-gas) #Quantum, superfluid, helium dynamics
paper · pdf · doi:10.48550/arxiv.2311.06507
openalex publication_date 2023/11/11 · openalex created_date 2023/11/15 · openalex updated_date 2026/07/28
In the mean-field approximation, the well-known effect of the critical quantum collapse in a 3D gas of particles pulled to the center by potential U(r) = -U0/r2 is suppressed by repulsive interparticle interactions, which create the otherwise non-existing s-wave ground state. Here, we address excited bound states carrying angular momentum, with the orbital and magnetic quantum numbers, l and m. They exist above a threshold value of the potential's strength, U0 > l(l+1). The sectoral, tesseral, and zonal modes, which correspond to m = l, 0 < m < l, and m = 0, respectively, are found in an approximate analytical form for relatively small values of U0 - l(l+1). Explicit results are produced for the p- and d-wave states, with l = 1 and 2, respectively. In the general form, the bound states are obtained numerically, confirming the accuracy of the analytical approximation.