Analysis on Schroedinger operators with delta-like magnetic fields on Riemannian manifolds

黎曼流形上类δ磁场薛定谔算子分析

• 批准号: 23740122
• 负责人: MINE Takuya
• 金额: $ 2.16万
• 依托单位: Kyoto Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23740122/
• 关键词: 数理物理; 関数方程式; 関数解析学; シュレディンガー方程式; アハラノフ・ボーム効果; 量子力学; 関数方程式論; シュレディンガ－方程式; ランダム・シュレディンガー作用素; 特殊函数; スペクトル幾何; 双曲平面上の量子力学; ベーテ・ゾンマーフェルト予想; ランダムシュレディンガー作用素

The Aharonov-Bohm effect is known as an observable quantum effect by the magnetic vector potential, which is introduced in the classical electrodynamics only as a computational tool. In this subject, we study the effect of the Aharonov-Bohm magnetic fields (delta-like magnetic fields) on the spectrum of the Schroedinger operators on Riemannian manifolds. Especially, we consider the Schroedinger operators on the hyperbolic plane with a constant magnetic field plus the Aharonov-Bohm magnetic fields placed periodically on a hyperbolic lattice, and study the threshold value of the magnetic fluxes for the existence of the infinitely degenerated Landau levels. Moreover, we consider the Schroedinger operators on the Euclidean plane with two quantized Aharonov-Bohm magnetic fields, and give an explicit form of the eigenfunctions in terms of the Mathieu functions.

Aharonov-Bohm效应是通过磁矢势可观测到的量子效应，磁矢势在经典电动力学中仅作为计算工具引入。在本课题中，我们研究了Aharonov-Bohm磁场（类δ磁场）对Riemannian流形上Schroedinger算子谱的影响。特别地，我们考虑了双曲平面上的Schroedinger算子，在双曲晶格上周期性地放置Aharonov-Bohm磁场和恒定磁场，研究了无限简并朗道能级存在的磁通阈值.此外，我们还考虑了两个量子化Aharonov-Bohm磁场下的Euclidean平面上的Schroedinger算子，并给出了本征函数的Mathieu函数的显式表示。

项目成果

Solvable models in two-solenoidal Aharonov-Bohm magnetic fields on the Euclidean plane, in Spectral and Scattering theory and Related Topics (ed. F. Hiroshima)

欧几里德平面上两个螺线管阿哈罗诺夫-玻姆磁场中的可解模型，光谱和散射理论及相关主题（F. Hiroshima 编）

• 发表时间: 2014
• 期刊: 数理解析研究所講究録別冊B
• 作者: Samuel Senti;Hiroki Takahasi;Hiromichi Ohno;Samuel Senti and Hiroki Takahasi;大野博道;大野 博道;Samuel Senti and Hiroki Takahasi;Yong Moo Chung and Hiroki Takahasi;Takuya Mine
• 通讯作者: Takuya Mine

Upper Bound for the Bethe–Sommerfeld Threshold and the Spectrum of the Poisson Random Hamiltonian in Two Dimensions

贝特-索末菲阈值的上限和二维泊松随机哈密顿量的谱

• DOI: 10.1007/s00023-012-0180-1
• 发表时间: 2013
• 期刊: Annales Henri Poincaré
• 作者: M. Kaminaga;T. Mine
• 通讯作者: T. Mine

京都工芸繊維大学 研究者総覧データベースシステム

京都工业大学研究员名录数据库系统

Landau levels on the hyperbolic plane in the presence of Aharonov–Bohm fields

存在阿哈罗诺夫-玻姆场时双曲平面上的朗道能级

• DOI: 10.1016/j.jfa.2012.06.002
• 发表时间: 2012
• 期刊: Journal of Functional Analysis
• 影响因子: 1.7
• 作者: T. Mine;Yuji Nomura
• 通讯作者: Yuji Nomura

楕円座標を用いた散乱振幅の計算

使用椭圆坐标计算散射幅度

• 发表时间: 2014
• 作者: Samuel Senti;Hiroki Takahasi;Hiromichi Ohno;Samuel Senti and Hiroki Takahasi;大野博道;大野 博道;Samuel Senti and Hiroki Takahasi;Yong Moo Chung and Hiroki Takahasi;Takuya Mine;Hiroki Takahasi;Masahiro Kaminaga and Takuya Mine;Hiroki Takahasi;Takuya Mine and Yuji Nomura;Hiroki Takahasi and Qiudong Wang;Masahiro Kaminaga and Takuya Mine;Manabu AKAHO;Hiroki Takahasi and Yong Moo Chung;峯 拓矢
• 通讯作者: 峯 拓矢