Accurate eigenvalue asymptotics for the magnetic Neumann Laplacian (Q818297)

The paper deals with the study of eigenvalues near the bottom of the spectrum of the magnetic Schrödinger operator with Neumann boundary conditions in a smooth, bounded domain \(\Omega\): \[ D(\mathcal{H})\ni u \rightarrowtail \mathcal{H}u = \mathcal{H}_{h,\Omega}u = (-ih\nabla_z-A(z))^2u(z), \] where \(A(z)\) is a vector potential generating a constant magnetic field with \(\operatorname{curl} A = 1\) and \[ D(\mathcal{H}) =\{u\in H^2(\Omega) | \nu \cdot (-ih\nabla_z - A(z))u| _{\partial\Omega}=0\}. \] The main result of the paper gives the asymptotic expansion of the lowest eigenvalues of \(\mathcal{H}\). The results are interesting from the point of view of their applications to superconductivity.