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arXiv · 2310.11928

Existence and Asymptotic Behavior of Minimizers for Rotating Bose-Einstein Condensations in Bounded Domains

Yongshuai Gao·Shuai Li·Peiye Zhong
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Abstract

This paper is concerned with the existence and mass concentration behavior of minimizers for rotating Bose-Einstein condensations (BECs) with attractive interactions in a bounded domain $\mathcal{D}\subset \mathbb{R}^2$. It is shown that, there exists a finite constant $a^*$, denoting mainly the critical number of bosons in the system, such that the least energy $e(a)$ admits minimizers if and only if $0<a<a^*$, no matter the trapping potential $V(x)$ rotates at any velocity $Ω\geq0$. This is quite different from the rotating BECs in the whole plane case, where the existence conclusions depend on the value of $Ω$ (cf. \cite[Theorem 1.1]{GLY}). Moreover, by establishing the refined estimates of the rotation term and the least energy, we also analyze the mass concentration behavior of minimizers in a harmonic potential as $a\nearrow a^*$.

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Yongshuai Gao, Shuai Li, Peiye Zhong. 2023-10-18. Existence and Asymptotic Behavior of Minimizers for Rotating Bose-Einstein Condensations in Bounded Domains. https://arxiv.org/abs/2310.11928

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