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Pré-Publication, Document De Travail Année : 2024

Gyrokinetic limit of the 2D Hartree equation in a large magnetic field

Résumé

We study the dynamics of two-dimensional interacting fermions submitted to a homogeneous transverse magnetic field. We consider a large magnetic field regime, with the gap between Landau levels set to the same order as that of potential energy contributions. Within the mean-field approximation, i.e. starting from Hartree's equation for the first reduced density matrix, we derive a drift equation for the particle density. We use vortex coherent states and the associated Husimi function to define a semi-classical density almost satisfying the limiting equation. We then deduce convergence of the density of the true Hartree solution by a Dobrushin-type stability estimate for the limiting equation.
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Dates et versions

hal-04523429 , version 1 (27-03-2024)
hal-04523429 , version 2 (11-04-2024)

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Denis Périce, Nicolas Rougerie. Gyrokinetic limit of the 2D Hartree equation in a large magnetic field. 2024. ⟨hal-04523429v2⟩
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