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

This paper is devoted to the numerical analysis of the Hermite spectral method proposed in the work of Filbet and Golse [J. Comput. Phys. 527 (2025), p. 20], 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.