均匀磁场中一个Aharonov-Bohm螺线管Schrödinger方程的色散和Strichartz估计

IF 1.3 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Annales Henri Poincaré Pub Date : 2024-10-28 DOI:10.1007/s00023-024-01500-8

Haoran Wang, Fang Zhang, Junyong Zhang

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引用次数: 0

摘要

我们得到了均匀磁场中一个Aharonov-Bohm螺线管Schrödinger方程解的色散估计和Strichartz估计。证明的主要步骤是构建Schrödinger核，而主要的障碍是获得核的显式表示，这需要大量的仔细计算。为了克服这个障碍，我们计划用两种不同的策略来构建Schrödinger内核。第一种是使用泊松求和公式，如Fanelli等人（Adv Math 400:108333, 2022），而第二种是依靠Št 'ovíček中的Schulman-Sunada公式（Ann Phys 376:254-282, 2017），该公式揭示了流形上的热核与群体行为的内在联系。

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

We obtain dispersive and Strichartz estimates for solutions to the Schrödinger equation with one Aharonov–Bohm solenoid in the uniform magnetic field. The main step of the proof is the construction of the Schrödinger 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 Schrödinger 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 Št’ovíček (Ann Phys 376:254–282, 2017), which reveals the intrinsic connections of the heat kernels on manifolds with group actions.

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来源期刊

Annales Henri Poincaré 物理-物理：粒子与场物理

CiteScore

3.00

自引率

6.70%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The two journals Annales de l''Institut Henri Poincaré, physique théorique and Helvetica Physical Acta merged into a single new journal under the name Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics edited jointly by the Institut Henri Poincaré and by the Swiss Physical Society. The goal of the journal is to serve the international scientific community in theoretical and mathematical physics by collecting and publishing original research papers meeting the highest professional standards in the field. The emphasis will be on analytical theoretical and mathematical physics in a broad sense.