This work presents a numerical analysis of a master equation modeling the interaction of a system with a noisy environment in the particular context of open quantum systems. It is shown that our transformed master equation has a reduced computational cost in comparison to a Wigner-Fokker-Planck model of the same system for the general case of any potential. Specifics of a NIPG-DG numerical scheme adequate for the convection-diffusion system obtained are then presented. This will let us solve computationally the transformed system of interest modeling our open quantum system. A benchmark problem, the case of a harmonic potential, is then presented, for which the numerical results are compared against the analytical steady-state solution of this problem.

翻译：本文针对开放量子系统中系统与噪声环境相互作用的特定场景，对一类主方程进行了数值分析。研究表明，对于任意势能的一般情况，相较于描述同一系统的Wigner-Fokker-Planck模型，我们提出的变换主方程具有更低的计算成本。随后给出了适用于所得对流-扩散系统的NIPG-DG数值格式的具体构造方法，从而能够通过数值计算求解描述开放量子系统的变换主方程。最后，以谐振势为例作为基准算题，将数值结果与该问题的解析稳态解进行了对比验证。