Magnetic bottles on the Poincaré half-plane: spectral asymptotics

Abstract

We consider a magnetic Laplacian $-\Delta_A=(id+A)^{\star} (id+A)$ on the Poincaré upper-half plane $mathbb{H}$ when the magnetic field $dA$ is infinite at the infinity such that $-\Delta_A$ has pure discret spectrum. We give the asymptotic behavior of the counting function of the eigenvalues.