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

被引：0
|
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 | 2024年
基金：
北京市自然科学基金; 中国国家自然科学基金;
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.
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页数：26
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