Eigenstates of the Neumann magnetic Laplacian with vanishing magnetic field
The paper is concerned with the spectral analysis of the magnetic Laplace operator with semiclassical positive parameter \(h>0\). This study is performed in the framework of bounded domains with smooth boundary in \(\mathbb {R}^2\) with Neumann magnetic boundary condition. A feature of this paper is that the magnetic field is assumed to vanish along a smooth curve intersecting the boundary. The main results of this paper describe the asymptotic behavior of the eigenvalues and the associated eigenfunctions when the semiclassical parameter \(h\) tends to \(0\).
scientific article; zbMATH DE number 6910612
scientific article