能量临界情况下具有谐波势的格罗斯-皮塔耶夫斯基方程的基态

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-28 DOI:10.3233/asy-241897

Dmitry E. Pelinovsky, Szymon Sobieszek

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引用次数: 0

摘要

具有谐波势的能量临界格罗斯-皮塔耶夫斯基方程的基态可以通过变分法构建。它存在于特征值参数的有限区间内。我们探索了大规范极限下的射影法，证明基态在近场点上接近于能量临界波方程的奥宾-塔伦提解，在远场点上接近于汇合超几何函数。射影法给出了特征值参数与上界规范的精确依赖关系。

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Ground state of the Gross–Pitaevskii equation with a harmonic potential in the energy-critical case

Ground state of the energy-critical Gross–Pitaevskii equation with a harmonic potential can be constructed variationally. It exists in a finite interval of the eigenvalue parameter. The supremum norm of the ground state vanishes at one end of this interval and diverges to infinity at the other end.We explore the shooting method in the limit of large norm to prove that the ground state is pointwise close to the Aubin–Talenti solution of the energy-critical wave equation in near field and to the confluent hypergeometric function in far field. The shooting method gives the precise dependence of the eigenvalue parameter versus the supremum norm.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.