发表机构
Faculty of Mathematics and Computer Science, University of Science, Ho Chi Minh City, Vietnam; Vietnam National University, Ho Chi Minh City, Vietnam; Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam（胡志明市科学大学数学与计算机科学学院; 胡志明市越南国立大学; 胡志明市栋塔大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对低维空间中含两体吸引、三体排斥的均匀玻色气体，研究其能量泛函极小化子的存在性，推导类托马斯-费米有效模型并分析其他极限 regime。
AI 中文摘要
在空间维数满足 $d \leq 2$ 的整个低维空间中，我们研究含吸引三次非线性项与排斥五次非线性项的能量泛函的极小化子，该泛函描述了具有两体吸引和三体排斥的量子玻色气体。我们证明了固定有效统计参数下极小化子的存在性。在质量临界非线性项（相对于动能）的有效统计参数很大的极限下，我们推导了均匀玻色气体的类托马斯-费米有效模型。我们还考虑了依赖于质量临界非线性项的其他极限 regime。
英文摘要
In the whole space of low spatial dimensions, namely $d \leq 2$, 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.
Journal refVietnam Journal of Mathematics (2026)
DOI：10.1007/s10013-026-00811-z
