论文标题
在旋转Anharmonic陷阱中，有吸引力的玻色气的基态
Ground States of Attractive Bose Gases in Rotating Anharmonic Traps
论文作者
论文摘要
本文涉及限制在Anharmonic陷阱$ V（x）=ω（| x |^2+k | x |^4）$上以速度$ω> 0 $旋转的吸引力的bose气体的基态，其中$ω> 0 $表示陷阱频率，$ k> 0 $代表了激烈的术语的强度。众所周知，对于任何$ω> 0 $，当且仅当$ 0 <a <a^*$，其中$ a^*：= \ | q \ |^{2} _ {2} $和$ q> 0 $是$ q+q^q+q^{3} = 0 $ in $ n $ in $ \ bb^2 $ n $ n $ n $ n $^2 $ {rbb {c^2通过分析基态的精致能量和扩展，我们证明存在常数$ c> 0 $，独立于$ 0 <a <a^*$，因此基态在$ r（a）中没有任何涡流： c（a^* - a）^{ - \ frac {1-6β} {20}} \ big \} $ as $ a \ nearrow a^*$，对于$ ch = \ frac {3Ω^2} {4} {4} {4} {4} $，$ k = \ frac {1} $ k = \ frac {1} $ {1} $ $ω= c_0（a^* - a）^{ - β} $在[0，\ frac {1} {6} {6}）$和$ c_0> 0 $的$β\中有所不同。
This paper is concerned with ground states of attractive Bose gases confined in an anharmonic trap $V(x)=ω(|x|^2+k|x|^4)$ rotating at the velocity $Ω>0$, where $ω>0$ denotes the trapping frequency, and $k>0$ represents the strength of the quartic term. It is known that for any $Ω>0$, ground states exist in such traps if and only if $0<a<a^*$, where $a^*:=\|Q\|^{2}_{2}$ and $Q>0$ is the unique positive solution of $ΔQ-Q+Q^{3}=0$ in $\mathbb{R}^2$. By analyzing the refined energies and expansions of ground states, we prove that there exists a constant $C>0$, independent of $0<a<a^*$, such that ground states do not have any vortex in the region $R(a):=\big\{x\in\mathbb{R}^2:\, |x|\leq C(a^*-a)^{-\frac{1-6β}{20}}\big\}$ as $a\nearrow a^*$, for the case where $ω=\frac{3Ω^2}{4}$, $k=\frac{1}{6}$, and $Ω=C_0(a^*-a)^{-β}$ varies for some $β\in [0,\frac{1}{6})$ and $C_0>0$.
