From the Laplacian with variable magnetic field to the electric Laplacian in the semiclassical limit

Abstract

We consider a twisted magnetic Laplacian with Neumann condition on a smooth and bounded domain of ${ℝ}^2$ in the semiclassical limit $h\to 0$. Under generic assumptions, we prove that the eigenvalues admit a complete asymptotic expansion in powers of $h^{1∕4}$.