Condensation and Collapse in the Mean-Field Limit of Rotating 2D Bose Gases with Two-Body and Three-Body Interactions
Abstract
We consider a system of N interacting bosons in a rotating harmonic trap in ℝ2, where the two-body interaction is attractive and scaled as N2αU(Nαx) with 0<α<1/12, and the three-body interaction is repulsive and scaled as N4βW(Nβx,Nβy) with 0<β<1/24. In the mean-field limit, the ground state energy is effectively described by a rotating cubic-quintic nonlinear Schrödinger functional. We analyze the collapse regime where the two-body coupling a approaches the critical value a* and the three-body coupling b tends to zero. The NLS ground states blow up with a universal profile given by the optimizer of the Gagliardo-Nirenberg inequality, and the energy satisfies ENLS = (1−ζ/4+o(1))𝒬potℓn2 with ζgeqslant0 determined by the relative rates of an→ a* and bnsearrow0. From the many-body theory, we rigorously justify this effective description: the quantum ground state energy converges to the NLS energy with the same asymptotic expansion in the collapse regime, and the many-body ground states exhibit complete Bose-Einstein condensation onto the universal blow-up profile.
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BibTeX
@misc{li2026condensation,
title = {{Condensation and Collapse in the Mean-Field Limit of Rotating 2D Bose Gases with Two-Body and Three-Body Interactions}},
author = {Deke Li and Yuan Li and Qingxuan Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06466},
eprint = {2609.06466},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06466},
}
RIS
TY - UNPB
TI - Condensation and Collapse in the Mean-Field Limit of Rotating 2D Bose Gases with Two-Body and Three-Body Interactions
AU - Deke Li
AU - Yuan Li
AU - Qingxuan Wang
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06466
UR - https://arxiv.org/abs/2609.06466
AB - We consider a system of N interacting bosons in a rotating harmonic trap in ℝ^2, where the two-body interaction is attractive and scaled as N^2αU(N^αx) with 0<α<1/12, and the three-body interaction is repulsive and scaled as N^4βW(N^βx,N^βy) with 0<β<1/24. In the mean-field limit, the ground state energy is effectively described by a rotating cubic-quintic nonlinear Schrödinger functional. We analyze the collapse regime where the two-body coupling a approaches the critical value a_* and the three-body coupling b tends to zero. The NLS ground states blow up with a universal profile given by the optimizer of the Gagliardo-Nirenberg inequality, and the energy satisfies E^NLS = (1−ζ/4+o(1))𝒬potℓ_n^2 with ζgeqslant0 determined by the relative rates of a_n→ a_* and b_nsearrow0. From the many-body theory, we rigorously justify this effective description: the quantum ground state energy converges to the NLS energy with the same asymptotic expansion in the collapse regime, and the many-body ground states exhibit complete Bose-Einstein condensation onto the universal blow-up profile.
ER -