The nonexistence of vortices for rotating Bose-Einstein condensates in non-radially symmetric traps

Guo, Yujin

doi:10.1016/j.matpur.2022.12.001

Cited by 5 publications

(4 citation statements)

References 57 publications

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“…See also [2]. Recently, in [4,8], Guo et al investigated the rotating Bose-Einstein condensates. For u : R N → C (N ≥ 2), the term…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

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Some remarks on the magnetic field operators \nabla±iA and its applications

WANG

2024

Proc. Rom. Acad. Ser. A - Math. Phys. Tech. Sci. Inf. Sci.

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In the present paper, we give some remarks on the magnetic field operators $\nabla \pm iA$. As its applications, we study the Schr\"{o}dinger equation with a magnetic field \begin{equation*} -\Delta u+|A(x)|^{2}u+iA(x)\cdot \nabla u=\mu u+|u|^{p}u,~x\in \mathbb{R}^{N}, \end{equation*} where $u$ is a complex-valued function and $\mu\in \mathbb{R}$. When $N>2$, for $2 p+2 \frac{2N}{N-2}$ or $N=2$, for $2 p+2 +\infty$, the existence and nonexistence of minimizers of the corresponding minimization problem are given via constrained variational methods. As a by-product, the above equation admits a normalized solution. We point out that the condition ${div}A(x)=0$ plays a crucial role in our study.

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“…See also [2]. Recently, in [4,8], Guo et al investigated the rotating Bose-Einstein condensates. For u : R N → C (N ≥ 2), the term…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…In rotating Bose-Einstein condensates, Ω describes the fixed rotational velocity (cf. [4] or [8]). Applying Lemma 1, we get the result as (2.4) in [8], i.e.,…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Some remarks on the magnetic field operators \nabla±iA and its applications

WANG

2024

Proc. Rom. Acad. Ser. A - Math. Phys. Tech. Sci. Inf. Sci.

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“…[9,16,18,19,20]) related to the variational problem (1.4). In particular, when there is no logarithmic convolution term in (1.4), Guo and his collaborators [16,19,20] studied various quantitative properties of minimizers for (1.4). In addition, Guo, Liang and Li [18] studied the existence and uniqueness of minimizers for (1.4) with Ω = 0 and V (x) = ln(1 + |x| 2 ).…”

mentioning

confidence: 99%

“…In recent years, there are many results (cf. [9,16,18,19,20]) related to the variational problem (1.4). In particular, when there is no logarithmic convolution term in (1.4), Guo and his collaborators [16,19,20] studied various quantitative properties of minimizers for (1.4).…”

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confidence: 99%

Core Content Selection and Textbook Design for High School Mathematics

Zhang¹,

Zhou²,

Wang³

et al. 2021

School Mathematics Textbooks in China

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This paper is devoted to studying the following fractional L 2 -critical nonlinear Schrödinger equation≥ 0 is an external potential. We obtain normalized L 2 -norm solutions of the above equation by solving the associated constraint minimization problem (1.4). It shows that there is a threshold a * > 0 such that (1.4) has minimizers for 0 < a < a * , and minimizers do not exist for any a > a * . For the case of a = a * , it gives a fact that the existence and non-existence of minimizers depend strongly on the value of V (0). Especially for V (0) = 0, we prove that minimizers occur blow-up behavior and the mass of minimizers concentrates at the origin as a ր a * . Applying implicit function theorem, the uniqueness of minimizers is also proved for a > 0 small enough.

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