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arXiv · 2507.16300

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

Théotime Girardot
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Abstract

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- Schr\"odinger 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.

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Théotime Girardot. 2025-07-22. 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. https://arxiv.org/abs/2507.16300

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