标题： 关于半经典极限下冯·诺依曼方程的逼近。 第二部分：数值分析 显示英文标题

标题： On the approximation of the von Neumann equation in the semi-classical limit. Part II : numerical analysis

摘要： 本文致力于分析[14]中提出的Hermite谱方法，该方法在半经典极限下提供了von Neumann方程的一种渐近保持逼近。 更具体地说，它依赖于所谓的Weyl变量的使用，以有效处理方程所关联的刚性问题。 然后通过采用密度算子的截断Hermite展开，我们成功地解决了这一刚性问题，并利用精确解的正则性传播提供了误差估计。 显示英文摘要

摘要： This paper is devoted to the numerical analysis of the Hermite spectral method proposed in [14], which provides, in the semi-classical 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.