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 $L^p\loc(\R^d)$, and with magnetic potentials in ${L^{q}\loc(\R^d)}$, where $p>\max (2d/3,2)$ and $q>2d$. For this purpose, we prove a singular Carleman estimate involving fractional Laplacian operators.

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Cited by in corpus (9)

• Unique continuation for many-body Schrödinger operators and the Hohenberg-Kohn theorem
• The structure of the density-potential mapping. Part I: Standard density-functional theory
• Universal Functionals in Density Functional Theory
• Building Kohn-Sham potentials for ground and excited states
• The structure of the density-potential mapping. Part II: Including magnetic fields
• Some properties of the potential-to-ground state map in quantum mechanics
• Twelve Tales in Mathematical Physics: An Expanded Heinemann Prize Lecture
• Quantum-Electrodynamical Density-Functional Theory Exemplified by the Quantum Rabi Model
• Density-functional theory for the Dicke Hamiltonian