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Semiclassical 3D Neumann Laplacian with variable magnetic field: a toy model
- Source :
- Communications in Partial Differential Equations, Communications in Partial Differential Equations, Taylor & Francis, 2012, 37 (9), pp.1528-1552. 〈10.1080/03605302.2012.680558〉, Communications in Partial Differential Equations, 2012, 37 (9), pp.1528-1552. ⟨10.1080/03605302.2012.680558⟩, Communications in Partial Differential Equations, Taylor & Francis, 2012, 37 (9), pp.1528-1552. ⟨10.1080/03605302.2012.680558⟩
- Publication Year :
- 2012
- Publisher :
- HAL CCSD, 2012.
-
Abstract
- 25 pages; International audience; 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.
- Subjects :
- Spectral theory
Semiclassical physics
01 natural sciences
[ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP]
[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
0101 mathematics
Eigenvalues and eigenvectors
Mathematics
Toy model
Applied Mathematics
Operator (physics)
010102 general mathematics
Mathematical analysis
[ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]
35P15, 35J15, 81Q20
Magnetic Laplacian
spectral theory
Eigenfunction
Mathematics::Spectral Theory
010101 applied mathematics
Agmon estimates
Asymptotic expansion
Laplace operator
Analysis
semiclassical analysis
Subjects
Details
- Language :
- English
- ISSN :
- 03605302 and 15324133
- Database :
- OpenAIRE
- Journal :
- Communications in Partial Differential Equations, Communications in Partial Differential Equations, Taylor & Francis, 2012, 37 (9), pp.1528-1552. 〈10.1080/03605302.2012.680558〉, Communications in Partial Differential Equations, 2012, 37 (9), pp.1528-1552. ⟨10.1080/03605302.2012.680558⟩, Communications in Partial Differential Equations, Taylor & Francis, 2012, 37 (9), pp.1528-1552. ⟨10.1080/03605302.2012.680558⟩
- Accession number :
- edsair.doi.dedup.....b3be35798b2b5c15e4e5ce03113d6c3f