Unique continuation for many-body Schrödinger operators and the Hohenberg-Kohn theorem. II. The Pauli Hamiltonian
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arXiv
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866917713080745984 |
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| author | Garrigue, Louis |
| author_facet | Garrigue, Louis |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1901_03207 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Unique continuation for many-body Schrödinger operators and the Hohenberg-Kohn theorem. II. The Pauli Hamiltonian Garrigue, Louis Mathematical Physics Analysis of PDEs Quantum Physics 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. |
| title | Unique continuation for many-body Schrödinger operators and the Hohenberg-Kohn theorem. II. The Pauli Hamiltonian |
| topic | Mathematical Physics Analysis of PDEs Quantum Physics |
| url | https://arxiv.org/abs/1901.03207 |