二维加权 CLR 类型界限

IF 1.2 2区数学 Q1 MATHEMATICS

Transactions of the American Mathematical Society 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

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.