含量子涨落和三体相互作用的3d偶极玻色-爱因斯坦凝聚
On 3d dipolar Bose-Einstein condensates involving quantum fluctuations and three-body interactions
摘要：
我们研究了以下非局部混合阶Gross-Pitaevskii方程$$i\,\partial_t ψ=-\frac{1}{2}\,Δψ+V_{ext}\,ψ+λ_1\,|ψ|^2\,ψ+λ_2\,(K*|ψ|^2)\,ψ+λ_3\,|ψ|^{p-2}\,ψ,$$其中$K$是经典偶极-偶极相互作用核，$λ_3>0$和$p\in(4,6]$，其中$p=6$是能量临界的.对于$p=5$，该方程被认为是目前描述偶极玻色-爱因斯坦凝聚动力学的最先进的模型（Lee-Huang-Yang校正的偶极GPE）。我们证明存在和不存在的驻波在不同的参数制度，$p\neq 6$，我们证明了全球适定性和小数据散射。
英文摘要：
We study the following nonlocal mixed order Gross-Pitaevskii equation $$i\,\partial_t ψ=-\frac{1}{2}\,Δψ+V_{ext}\,ψ+λ_1\,|ψ|^2\,ψ+λ_2\,(K*|ψ|^2)\,ψ+λ_3\,|ψ|^{p-2}\,ψ,$$ where $K$ is the classical dipole-dipole interaction kernel, $λ_3>0$ and $p\in(4,6]$; the case $p=6$ being energy critical. For $p=5$ the equation is considered currently as the state-of-the-art model for describing the dynamics of dipolar Bose-Einstein condensates (Lee-Huang-Yang corrected dipolar GPE). We prove existence and nonexistence of standing waves in different parameter regimes; for $p\neq 6$ we prove global well-posedness and small data scattering.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
