Free and Harmonic Trapped Spin-1 Bose–Einstein Condensates in [math]

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-07-01 DOI:10.1137/23m1572222

Menghui Li, Xiao Luo, Juncheng Wei, Maoding Zhen

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引用次数: 0

Abstract

SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 4375-4414, August 2024.
Abstract. We investigate physical states of spin-1 Bose–Einstein condensate in [math] with mean-field interaction constant [math] and spin-exchange interaction constant [math], two conserved quantities, the number of atoms [math], and the total magnetization [math] are involved in. First, in the free case, existence and asymptotic behavior of ground states are analyzed according to the relations among [math], [math], [math], and [math]. Furthermore, we show that the corresponding standing wave is strongly unstable. When the atoms are trapped in a harmonic potential, we prove the existence of ground states and excited states along with some precisely asymptotics. Besides, we get that the set of ground states is stable under the associated Cauchy flow while the excited state corresponds to a strongly unstable standing wave. Our results not only show some characteristics of three-dimensional spin-1 BEC under the effect between the spin-dependent interaction and the external magnetic field, but also support some experimental observations as well as numerical results on spin-1 BEC.

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数学]中的自由和谐波陷波自旋-1 玻色-爱因斯坦凝聚态

SIAM 数学分析期刊》，第 56 卷第 4 期，第 4375-4414 页，2024 年 8 月。摘要。我们研究了具有均场相互作用常数[math]和自旋交换相互作用常数[math]的[math]中自旋-1玻色-爱因斯坦凝聚态的物理状态，其中涉及两个守恒量原子数[math]和总磁化率[math]。首先，在自由情况下，根据[math]、[math]、[math]和[math]之间的关系分析了基态的存在和渐近行为。此外，我们还证明了相应的驻波具有强烈的不稳定性。当原子被困在谐波势中时，我们证明了基态和激发态的存在，以及一些精确的渐近线。此外，我们还得到了基态集合在相关考奇流下是稳定的，而激发态则对应于强不稳定驻波。我们的结果不仅显示了三维自旋-1 BEC 在自旋相关相互作用和外磁场作用下的一些特征，而且支持了自旋-1 BEC 的一些实验观察和数值结果。

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来源期刊

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.