二维加权 CLR 类型界限

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-01-25 DOI:10.1090/tran/9124

Rupert Frank, Ari Laptev, Larry Read

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引用次数: 0

摘要

我们推导了具有非难阿哈诺夫-玻姆磁场的二维薛定谔算子的加权版 Cwikel-Lieb-Rozenblum 不等式。我们的边界捕捉到了对磁通量的最佳依赖，并确定了一类在强耦合极限下能使我们的边界达到饱和的长程势。我们还将分析扩展到作用于反对称函数的二维薛定谔算子，并得到了类似的结果。

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Weighted CLR type bounds in two dimensions

We derive weighted versions of the Cwikel–Lieb–Rozenblum inequality for the Schrödinger operator in two dimensions with a nontrivial Aharonov–Bohm magnetic field. Our bounds capture the optimal dependence on the flux and we identify a class of long-range potentials that saturate our bounds in the strong coupling limit. We also extend our analysis to the two-dimensional Schrödinger operator acting on antisymmetric functions and obtain similar results.

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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.

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