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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.16300 |
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| _version_ | 1866912496522100736 |
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| author | Girardot, Théotime |
| author_facet | Girardot, Théotime |
| contents | We show that a 2-dimensional system of N fermions interacting through a pairwise electric and magnetic singular interactions with Slater initial data preserves its Slater structure over time when N gets large. In other words, the wave function of the system can be approximated by a Slater determinant whose orbitals evolves according to a coupled system of N Chern-Simons- Schrödinger type effective equations. The result holds in a dilute regime where the density is of order one on a large volume proportional to the number of particles. The pairwise magnetic feature of the system implies to deal with the diagonalization of three-body potentials which is the main mathematical innovation of the paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16300 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Derivation of the Hartree dynamics for a N-particles fermionic 2D system interacting via long-range electric and magnetic two-body singular potentials in a dilute regime Girardot, Théotime Mathematical Physics Quantum Gases We show that a 2-dimensional system of N fermions interacting through a pairwise electric and magnetic singular interactions with Slater initial data preserves its Slater structure over time when N gets large. In other words, the wave function of the system can be approximated by a Slater determinant whose orbitals evolves according to a coupled system of N Chern-Simons- Schrödinger type effective equations. The result holds in a dilute regime where the density is of order one on a large volume proportional to the number of particles. The pairwise magnetic feature of the system implies to deal with the diagonalization of three-body potentials which is the main mathematical innovation of the paper. |
| title | Derivation of the Hartree dynamics for a N-particles fermionic 2D system interacting via long-range electric and magnetic two-body singular potentials in a dilute regime |
| topic | Mathematical Physics Quantum Gases |
| url | https://arxiv.org/abs/2507.16300 |