Accurate eigenvalue asymptotics for the magnetic Neumann Laplacian

Eigenvalue Asymptotics of the Neumann Laplacian of Regions and Manifolds with Cusps

We study the eigenvalue asymptotics of a Neumann Laplacian-A$ in unbounded regions 0 of R2 with cusps at infinity (a typical example is a={(~, y)~R~:x>l, Iyl-ce-" I}) and prove that NE(A:)-NE(HY)+ E/2 Vol(Q), where HV is the canonical one-dimensional Schrodinger operator associated to the problem. We establish a similar formula for manifolds with cusps and derive the eigenvalue asymptotics of a...

Eigenvalue Asymptotics of the Even-Dimensional Exterior Landau-Neumann Hamiltonian

Magnetic Neumann Laplacian on a sharp cone

This paper is devoted to the spectral analysis of the Laplacian with constant magnetic field on a cone of aperture α and Neumann boundary condition. We analyze the influence of the orientation of the magnetic field. In particular, for any orientation of the magnetic field, we prove the existence of discrete spectrum below the essential spectrum in the limit α → 0 and establish a full asymptotic...

On the semiclassical 3D Neumann Laplacian with variable magnetic field

Eigenvalue asymptotics for magnetic fields and degenerate potentials