Semiclassical 3D Neumann Laplacian with Variable Magnetic Field: A Toy Model

In this paper we investigate the semiclassical behavior of the lowest eigenvalues of a model Schrödinger operator with variable magnetic field. This work aims at proving an accurate asymptotic expansion for these eigenvalues, the corresponding upper bound being already proved in the general case. Th...

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Bibliographic Details
Published in:Communications in partial differential equations 2012-09, Vol.37 (9), p.1528-1552
Main Author: Raymond, Nicolas
Format: Article
Language:English
Subjects:
35P
Agmon estimates
Analysis of PDEs
Magnetic Laplacian
Mathematical Physics
Mathematics
Semiclassical analysis
Spectral theory
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Summary:In this paper we investigate the semiclassical behavior of the lowest eigenvalues of a model Schrödinger operator with variable magnetic field. This work aims at proving an accurate asymptotic expansion for these eigenvalues, the corresponding upper bound being already proved in the general case. The present work also aims at establishing localization estimates for the attached eigenfunctions.
ISSN:0360-5302
1532-4133
DOI:10.1080/03605302.2012.680558