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arXiv · 2504.18177

On the approximation of the von Neumann equation in the semiclassical limit. Part II : numerical analysis

Francis Filbet·François Golse
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Abstract

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.

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Francis Filbet, François Golse. 2025-04-25. On the approximation of the von Neumann equation in the semiclassical limit. Part II : numerical analysis. https://arxiv.org/abs/2504.18177

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