On the approximation of the von Neumann equation in the semiclassical limit. Part II : numerical analysis
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917334035202048 |
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| author | Filbet, Francis Golse, François |
| author_facet | Filbet, Francis Golse, François |
| contents | This paper is devoted to the numerical analysis of the Hermite spectral method proposed in [14], which provides, in the semiclassical limit, an asymptotic preserving approximation of the von Neumann equation. More precisely, it relies on the use of so-called Weyl's variables to effectively address the stiffness associated to the equation. Then by employing a truncated Hermite expansion of the density operator, we successfully manage this stiffness and provide error estimates by leveraging the propagation of regularity in the exact solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18177 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the approximation of the von Neumann equation in the semiclassical limit. Part II : numerical analysis Filbet, Francis Golse, François Numerical Analysis This paper is devoted to the numerical analysis of the Hermite spectral method proposed in [14], which provides, in the semiclassical limit, an asymptotic preserving approximation of the von Neumann equation. More precisely, it relies on the use of so-called Weyl's variables to effectively address the stiffness associated to the equation. Then by employing a truncated Hermite expansion of the density operator, we successfully manage this stiffness and provide error estimates by leveraging the propagation of regularity in the exact solution. |
| title | On the approximation of the von Neumann equation in the semiclassical limit. Part II : numerical analysis |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2504.18177 |