Geodesic
Unique Continuation for Many-Body Schrödinger Operators and the Hohenberg-Kohn Theorem. II: The Pauli Hamiltonian
Documenta mathematica, Tome 25 (2020), pp. 869-898.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We prove the strong unique continuation property for many-body Pauli operators with external potentials, interaction potentials and magnetic fields in $L^p_{\mathrm{loc}}(\mathbb{R}^d)$, and with magnetic potentials in $L^q_{\mathrm{loc}}(\mathbb{R}^d)$, 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.
Classification : 35Q40, 81V70, 82M36, 35Q60, 35Q55, 35J05, 35R11, 26A33
Keywords: quantum mechanics, unique continuation, many-body theory, Hohenberg-Kohn theorem, density functional theory 
@article{DOCMA_2020__25__a42,
     author = {Garrigue, Louis},
     title = {Unique {Continuation} for {Many-Body} {Schr\"odinger} {Operators} and the {Hohenberg-Kohn} {Theorem.} {II:} {The} {Pauli} {Hamiltonian}},
     journal = {Documenta mathematica},
     pages = {869--898},
     publisher = {mathdoc},
     volume = {25},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a42/}
}
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Garrigue, Louis. Unique Continuation for Many-Body Schrödinger Operators and the Hohenberg-Kohn Theorem. II: The Pauli Hamiltonian. Documenta mathematica, Tome 25 (2020), pp. 869-898. http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a42/