Gyrokinetic limit of the 2D Hartree equation in a large magnetic field
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912762719895552 |
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| author | Périce, Denis Rougerie, Nicolas |
| author_facet | Périce, Denis Rougerie, Nicolas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19226 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gyrokinetic limit of the 2D Hartree equation in a large magnetic field Périce, Denis Rougerie, Nicolas Analysis of PDEs 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. |
| title | Gyrokinetic limit of the 2D Hartree equation in a large magnetic field |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.19226 |