Unique Continuation for Many-Body Schrödinger Operators and the Hohenberg-Kohn Theorem. II: The Pauli Hamiltonian

Abstract

We prove the strong unique continuation property for many-body Pauli operators with external potentials, interaction potentials and magnetic fields in $L_{\mathrm{loc}}^p({\mathbb{R}}^d)$, and with magnetic potentials in $L_{\mathrm{loc}}^q({\mathbb{R}}^d)$, where $p>\max (2d/3,2)$ and $q>2d$. For this purpose, we prove a singular Carleman estimate involving fractional Laplacian operators. Consequently, we obtain Tellgren's Hohenberg-Kohn theorem for the Maxwell-Schrödinger model.