Local Density Approximation and Other Limit Regimes for a Homogeneous Bose Gas with Repulsive Three-Body Interactions in Low-Dimensional Space

@misc{doan2026local,
  title = {{Local Density Approximation and Other Limit Regimes for a Homogeneous Bose Gas with Repulsive Three-Body Interactions in Low-Dimensional Space}},
  author = {Thi Anh Thu Doan and Dinh-Thi Nguyen},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.29876},
  eprint = {2608.29876},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29876},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Local Density Approximation and Other Limit Regimes for a Homogeneous Bose Gas with Repulsive Three-Body Interactions in Low-Dimensional Space
AU  - Thi Anh Thu Doan
AU  - Dinh-Thi Nguyen
PY  - 2026
DA  - 2026/08/30
PB  - arXiv
DO  - 10.48550/arxiv.2608.29876
UR  - https://arxiv.org/abs/2608.29876
AB  - In the whole space of low spatial dimensions, namely d ≤ 2, we study the minimizers of an energy functional with an attractive cubic nonlinearity and a repulsive quintic nonlinearity, which describes a quantum Bose gas with a two-body attraction and a three-body repulsion. We prove the existence of minimizers at fixed effective statistics parameter. In the limit of a large effective statistics parameter of the mass-critical nonlinearity (with respect to the kinetic energy), we derive an effective Thomas-Fermi-like model for the homogeneous Bose gas. We also consider other limit regimes depending on the mass-critical nonlinearity.
ER  -