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| Autori principali: | , , , |
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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2503.16001 |
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| _version_ | 1866912285465772032 |
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| author | Benedikter, Niels Boccato, Chiara Monaco, Domenico Nguyen, Ngoc Nhi |
| author_facet | Benedikter, Niels Boccato, Chiara Monaco, Domenico Nguyen, Ngoc Nhi |
| contents | We study the quantum dynamics of a large number of interacting fermionic particles in a constant magnetic field. In a coupled mean-field and semiclassical scaling limit, we show that solutions of the many-body Schrödinger equation converge to solutions of a non-linear Hartree-Fock equation. The central ingredient of the proof are certain semiclassical trace norm estimates of commutators of the position and momentum operators with the one-particle density matrix of the solution of the Hartree-Fock equation. In a first step, we prove their validity for non-interacting initial data in a magnetic field by generalizing a 2020 result of Fournais and Mikkelsen. We then propagate these bounds from the initial data along the Hartree-Fock flow to arbitrary times. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_16001 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Derivation of Hartree-Fock Dynamics and Semiclassical Commutator Estimates for Fermions in a Magnetic Field Benedikter, Niels Boccato, Chiara Monaco, Domenico Nguyen, Ngoc Nhi Mathematical Physics We study the quantum dynamics of a large number of interacting fermionic particles in a constant magnetic field. In a coupled mean-field and semiclassical scaling limit, we show that solutions of the many-body Schrödinger equation converge to solutions of a non-linear Hartree-Fock equation. The central ingredient of the proof are certain semiclassical trace norm estimates of commutators of the position and momentum operators with the one-particle density matrix of the solution of the Hartree-Fock equation. In a first step, we prove their validity for non-interacting initial data in a magnetic field by generalizing a 2020 result of Fournais and Mikkelsen. We then propagate these bounds from the initial data along the Hartree-Fock flow to arbitrary times. |
| title | Derivation of Hartree-Fock Dynamics and Semiclassical Commutator Estimates for Fermions in a Magnetic Field |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2503.16001 |