Magnetic Bottles for the Neumann Problem: The Case of Dimension 3

Proceedings Mathematical Sciences

Abderemane Morame²  Bernard Helffer¹ 

[1] Département de Mathématiques, UMR CNRS , Bât. , Université Paris-Sud, F-0 Orsay Cedex, France$$;Département de Mathématiques, UMR CNRS , Université de Nantes, , rue de la Houssinière, B.P. 0, Nantes Cedex , France$$

关键词: Spectral theory;    Schrödinger operators;    magnetic fields;    superconductivity.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

The main object of this paper is to analyze the recent results obtained on the Neumann realization of the Schrödinger operator in the case of dimension 3 by Lu and Pan. After presenting a short treatment of their spectral analysis of key-models, we show briefly how to implement the techniques of Helffer–Morame in order to give some localization of the ground state. This leaves open the question of the localization by curvature effect which was solved in the case of dimension 2 in our previous work and will be analysed in the case of dimension 3 in a future paper.

【 授权许可】

Unknown