论文标题
旋转非圣对称陷阱中旋转Bose-Einstein冷凝水的涡流不存在
The Nonexistence of Vortices for Rotating Bose-Einstein Condensates in Non-Radially Symmetric Traps
论文作者
论文摘要
我们考虑旋转Bose-Einstein旋转的基态，并在非谐波谐波陷阱中具有有吸引力的相互作用$ v（x）= x_1^2+λ^2x_2^2 $，其中$ 0<λ\ not = 1 $ and $ x =（x_1，x_1，x_2）\ in R^2 $。 For any fixed rotational velocity $0\le Ω<Ω^*:=2\min \{1, Λ\}$, it is known that ground states exist if and only if $ a<a^*$ for some critical constant $0<a^*<\infty$, where $a>0$ denotes the product for the number of particles times the absolute value of the scattering length.我们将基础状态的渐近扩展分析为$ a \近a^*$，它显示了$ω$对基础状态的可见效果。作为副产品，我们进一步证明了基础状态在区域$ r（a）中没有任何涡流：= \ {x \ in r^2：\，| \，| x | \ le c（a^* - a^* - a）^{ - \ frac {1} {1} {12}}}}}}}}}} \} $ as $ a \ a \ a \ a \ a \ a \ a \ a \ a \ a is a^a^a^*$ c $ c> $ 0 <a <a^*$。
We consider ground states of rotating Bose-Einstein condensates with attractive interactions in non-radially harmonic traps $V(x)=x_1^2+Λ^2x_2^2 $, where $0<Λ\not =1$ and $x=(x_1, x_2)\in R^2$. For any fixed rotational velocity $0\le Ω<Ω^*:=2\min \{1, Λ\}$, it is known that ground states exist if and only if $ a<a^*$ for some critical constant $0<a^*<\infty$, where $a>0$ denotes the product for the number of particles times the absolute value of the scattering length. We analyze the asymptotic expansions of ground states as $a\nearrow a^*$, which display the visible effect of $Ω$ on ground states. As a byproduct, we further prove that ground states do not have any vortex in the region $R(a):=\{x\in R^2:\,|x|\le C (a^*-a)^{-\frac{1}{12}}\}$ as $a\nearrow a^*$ for some constant $C>0$, which is independent of $0<a<a^*$.
