Marwa Nasrallah: Energy of surface states for 3D magnetic (Neumann) Schrodinger operators

We prove an asymptotic formula for the energy of the sum of eigenvalues for a magnetic Schrodinger operator on a 3D domain (exterior or interior) with compact smooth boundary on which we impose the Neumann boundary condition. The approach relies on a careful analysis of the geometry where by straightening out the boundary the problem is reduced to the model case of the half-space. In particular, we show the existence of the thermodynamic limit in a cubic domain of the half-space and provide related explicit formulae in terms of the eigenvalues of model operators of the half-plane and the half-axis.