Singularities and asymptotic distribution of resonances for Schrödinger operators in one dimension

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-08 DOI:10.3233/asy-241928

T. J. Christiansen, T. Cunningham

引用次数: 0

Abstract

We obtain new results about the high-energy distribution of resonances for the one-dimensional Schrödinger operator. Our primary result is an upper bound on the density of resonances above any logarithmic curve in terms of the singular support of the potential. We also prove results about the distribution of resonances in sectors away from the real axis, and construct a class of potentials producing multiple sequences of resonances along distinct logarithmic curves, explicitly calculating the asymptotic location of these resonances. The results are unified by the use of an integral representation of the reflection coefficients, refining methods used in (J. Differential Equations 137(2) (1997) 251–272) and (J. Funct. Anal. 178(2) (2000) 396–420).

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一维薛定谔算子共振的奇异性和渐近分布

我们获得了一维薛定谔算子共振高能分布的新结果。我们的主要结果是，根据势的奇异支持，在任何对数曲线上方的共振密度的上界。我们还证明了远离实轴扇区的共振分布结果，并构建了一类沿着不同对数曲线产生多序列共振的势，明确计算了这些共振的渐近位置。通过使用反射系数的积分表示法，完善了《微分方程学报》（J. Differential Equations）137(2) (1997) 251-272 和《函数分析学报》（J. Funct. Anal.Anal.178(2) (2000) 396-420).

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.