References & Citations
Mathematics > Analysis of PDEs
Title: Gyrokinetic limit of the 2D Hartree equation in a large magnetic field
(Submitted on 28 Mar 2024 (v1), last revised 12 Apr 2024 (this version, v2))
Abstract: 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.
Submission history
From: Nicolas Rougerie [view email][v1] Thu, 28 Mar 2024 08:41:17 GMT (39kb)
[v2] Fri, 12 Apr 2024 07:09:13 GMT (39kb)
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