标题： 一个求解量子Liouville-BGK方程的渐近保持格式 显示英文标题

标题： An asymptotic preserving scheme for the quantum Liouville-BGK equation

摘要： 我们对这项工作中量子 Liouville-BGK 方程的数值求解感兴趣，该方程出现在从头推导量子流体力学模型的过程中。这类模型通常是在某些渐近极限下获得的，例如扩散极限或流体极限，因此原始的 Liouville 方程包含小参数。标准方法（如分步算法）在这种情况下只有当时间步长相对于渐近参数足够小时才准确，这是一个严重的限制。对于扩散极限情况，我们提出了一种对于与小参数无关的时间步长仍然准确的数值方法，并且能够很好地捕捉微观动力学和扩散极限。我们的方法通过非正式的理论误差分析得到了支持。 显示英文摘要

摘要： We are interested in this work in the numerical resolution of the Quantum Liouville-BGK equation, which arises in the derivation of quantum hydrodynamical models from first principles. Such models are often obtained in some asymptotic limits, for instance a diffusion or a fluid limit, and as a consequence the original Liouville equation contains small parameters. A standard method such as a split-step algorithm is then accurate provided the time step is sufficiently small compared to the asymptotic parameter, which is a severe limitation. In the case of the diffusion limit, we propose a numerical method that is accurate for time steps independent of the small parameter, and which captures well both the microscopic dynamics and the diffusion limit. Our approach is substantiated by an informal theoretical error analysis.