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

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

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 Helf...

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Veröffentlicht in:Proceedings of the Indian Academy of Sciences. Mathematical sciences 2002-02, Vol.112 (1), p.71-84
Hauptverfasser: Helffer, Bernard, Morame, Abderemane
Format: Artikel
Sprache:eng
Schlagworte:
Localization
Neumann problem
Operators (mathematics)
Spectrum analysis
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Zusammenfassung: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.
ISSN:0253-4142
0973-7685
DOI:10.1007/BF02829641