Magnetic bottles for the Neumann problem: The case of dimension 3

Article

DOI: 10.1007/BF02829641

Cite this article as:
Helffer, B. & Morame, A. Proc. Indian Acad. Sci. (Math. Sci.) (2002) 112: 71. doi:10.1007/BF02829641

Abstract

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 keymodels, 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.

Keywords

Spectral theory Schrödinger operators magnetic fields superconductivity 

Copyright information

© Printed in India 2002

Authors and Affiliations

  1. 1.Département de Mathématiques, UMR CNRS 8628, Bât. 425Université Paris-SudOrsay CedexFrance
  2. 2.Département de Mathématiques, UMR CNRS 6629Université de Nantes, 2, rue de la HoussinièreNantes Cedex 3France