Dispersive and Strichartz Estimates for Schrödinger Equation with One Aharonov-Bohm Solenoid in a Uniform Magnetic Field

被引：2

作者：

Wang, Haoran ^{[1
]}

Zhang, Fang ^{[1
]}

Zhang, Junyong ^{[1
]}

机构：

[1] Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China

来源：

ANNALES HENRI POINCARE | 2025年 / 26卷 / 08期

基金：

中国国家自然科学基金; 北京市自然科学基金;

关键词：

SCHRODINGER-OPERATORS; POTENTIALS; WAVE; DECAY;

D O I：

10.1007/s00023-024-01500-8

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We obtain dispersive and Strichartz estimates for solutions to the Schr & ouml;dinger equation with one Aharonov-Bohm solenoid in the uniform magnetic field. The main step of the proof is the construction of the Schr & ouml;dinger kernel, and the main obstacle is to obtain the explicit representation of the kernel, which requires a large set of careful calculations. To overcome this obstacle, we plan to construct the Schr & ouml;dinger kernel by two different strategies. The first one is to use the Poisson summation formula as Fanelli et al. (Adv Math 400:108333, 2022), while the second one relies on the Schulman-Sunada formula in & Scaron;t'ov & iacute;& ccaron;ek (Ann Phys 376:254-282, 2017), which reveals the intrinsic connections of the heat kernels on manifolds with group actions.

引用

页码：3029 / 3054

页数：26

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