Schrödinger Operators with Multiple Aharonov–Bohm Fluxes

IF 1.4 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Annales Henri Poincaré Pub Date : 2024-05-25 DOI:10.1007/s00023-024-01446-x

Michele Correggi, Davide Fermi

引用次数: 0

Abstract

We study the Schrödinger operator describing a two-dimensional quantum particle moving in the presence of \( N \geqslant 1\) Aharonov–Bohm magnetic fluxes. We classify all the self-adjont realizations of such an operator, providing an explicit characterization of their domains and actions. Moreover, we examine their spectral and scattering properties, proving in particular the existence and completeness of wave operators in relation with the free dynamics.

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具有多重阿哈诺夫-玻姆通量的薛定谔算子

我们研究了描述一个二维量子粒子在 \( N \geqslant 1\) Aharonov-Bohm 磁通量存在下运动的薛定谔算子。我们对这样一个算子的所有自增现实进行了分类，提供了它们的域和作用的明确表征。此外，我们还考察了它们的谱和散射特性，特别证明了与自由动力学相关的波算子的存在性和完备性。

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

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.