Research on spectrum of random magnetic Schr {"o} dinger operators

随机磁Schr {"o} dinger算子谱的研究

• 批准号: 17540148
• 负责人: NOMURA Yuji
• 金额: $ 0.96万
• 依托单位: Tokyo Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-17540148/
• 关键词: random magnetic field; Schr"odinger operator; spectrum; ラプラシアン; アーベル被覆グラフ

We consider the magnetic Schr"odinger operator on $mathbf{R}^2$. The magnetic field is the sum of a homogeneous magnetic field and periodically varying pointlike magnetic fields on a lattice. We shall give a sufficient condition for each Landau level to be an infinitely degenerated eigenvalue. This condition is also necessary for the lowest Landau level. In the threshold case, we see that the spectrum near the lowest Landau level is purely absolutely continuous. Moreover, we shall give an estimate for the density of states for Landau levels and their gaps. The proof is based on the method of Geyler and v Sv tov'iv cek, the magnetic Bloch theory, and canonical commutation relations.

我们考虑磁场上的磁性schr“ Odinger”操作员。磁场是均匀的磁场的总和，在晶格上定期变化的磁场，我们将为每个Landau级别提供足够的条件，使每个固定级别的特征级别都需要。最低的Landau级别纯粹是连续的，我们将对Landau级别的状态密度估算及其差距。

项目成果

Periodic Aharonov-Bohm Solenoids in a constant magnetic field

恒定磁场中的周期性阿哈罗诺夫-玻姆螺线管

• 发表时间: 2006
• 期刊: Reviews in mathematical physics Vol. 18, 8
• 作者: Mine Takuya;Yuji Nomura
• 通讯作者: Yuji Nomura