We show how to derive an effective nonlinear dynamics, described by the Hartree-Fock equations, for fermionic quantum particles confined to a two-dimensional box and in presence of an external, uniform magnetic field. The derivation invokes the Dirac-Frenkel principle. We discuss the validity of this effective description with respect to the many-body Schr\"odinger dynamics for small times and for weak interactions, and also in regards to the number of particles.
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Ferrero et al. (2024) studied this question.
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