Static States for Rotating Two-Component Bose–Einstein Condensates

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics Pub Date : 2025-01-25 DOI:10.1111/sapm.70013

Hichem Hajaiej, Xiao Luo, Tao Yang

{"title":"Static States for Rotating Two-Component Bose–Einstein Condensates","authors":"Hichem Hajaiej, Xiao Luo, Tao Yang","doi":"10.1111/sapm.70013","DOIUrl":null,"url":null,"abstract":"<div>\n \n In this paper, we study static states for rotating two-component Bose–Einstein condensates (BECs) in two and three dimensions. This leads to analyze normalized solutions for a coupled Schrödinger system with rotation. In dimension two, it corresponds to a mass-critical problem, for which we obtain some existence and nonexistence results. In the three-dimensional case, the problem becomes mass-supercritical, where we prove a multiplicity result along with an accurately asymptotical analysis. Furthermore, a stability result is also established in both cases. We not only extend the main results in Ardila and Hajaiej (Journal of Dynamics and Differential Equations 35 (2023), 1643–1665), Arbunich et al. (Letters in Mathematical Physics 109 (2019), 1415–1432), and Luo and Yang (Journal of Differential Equations 304 (2021), 326–347) from the rotating one-component BEC to rotating two-component BECs, but we also partially extend the results of Guo et al. (Discrete and Continuous Dynamical Systems 37 (2017), 3749–3786; Journal of Differential Equations 264 (2018), 1411–1441) from nonrotating two-component BECs to rotating two-component BECs.</div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6000,"publicationDate":"2025-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studies in Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/sapm.70013","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

Abstract

In this paper, we study static states for rotating two-component Bose–Einstein condensates (BECs) in two and three dimensions. This leads to analyze normalized solutions for a coupled Schrödinger system with rotation. In dimension two, it corresponds to a mass-critical problem, for which we obtain some existence and nonexistence results. In the three-dimensional case, the problem becomes mass-supercritical, where we prove a multiplicity result along with an accurately asymptotical analysis. Furthermore, a stability result is also established in both cases. We not only extend the main results in Ardila and Hajaiej (Journal of Dynamics and Differential Equations 35 (2023), 1643–1665), Arbunich et al. (Letters in Mathematical Physics 109 (2019), 1415–1432), and Luo and Yang (Journal of Differential Equations 304 (2021), 326–347) from the rotating one-component BEC to rotating two-component BECs, but we also partially extend the results of Guo et al. (Discrete and Continuous Dynamical Systems 37 (2017), 3749–3786; Journal of Differential Equations 264 (2018), 1411–1441) from nonrotating two-component BECs to rotating two-component BECs.

查看原文本刊更多论文

旋转双组分玻色-爱因斯坦凝聚体的静态

本文研究了二维和三维旋转双组分玻色-爱因斯坦凝聚体的静态。这导致了对旋转耦合Schrödinger系统的归一化解的分析。在二维中，它对应于一个质量临界问题，我们得到了一些存在性和不存在性的结果。在三维情况下，问题变成质量超临界，我们证明了多重性结果以及精确的渐近分析。此外，还建立了两种情况下的稳定性结果。我们不仅将Ardila和Hajaiej （Journal of Dynamics and Differential Equations 35(2023), 1643-1665）、Arbunich等人（Letters in Mathematical Physics 109(2019), 1415-1432）和Luo和Yang （Journal of Differential Equations 304(2021), 326-347）的主要结果从旋转单组分BEC扩展到旋转双组分BEC，而且我们还部分扩展了Guo等人(Discrete and Continuous Dynamical Systems 37 (2017), 3749-3786；微分方程学报，264(2018),1411-1441。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Studies in Applied Mathematics 数学-应用数学

CiteScore

4.30

自引率

3.70%

发文量

审稿时长

>12 weeks

期刊介绍： Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.