AI 中文总结
该研究扩展量子调制能量，从两类磁化量子方程推导出磁化无压欧拉-泊松方程，分析对应偏微分方程局部适定性，成果属磁化量子动力学极限研究范畴。
AI 中文摘要
我们扩展了文献[17]中提出的量子调制能量，分别从磁化薛定谔-泊松方程和冯·诺依曼方程推导出磁化无压欧拉-泊松方程，作为半经典极限和平均场半经典极限。本文还研究了对应的单动力学偏微分方程的局部适定性。在两种极限情形中，磁场均为外场且可随空间非均匀变化。我们的研究结果属于磁化量子动力学的半经典极限与量子平均场极限这一更广泛范畴。
英文摘要
We extend the quantum modulated energy developed in [17] in order to de- rive the magnetized pressureless Euler-Poisson equation as a semiclassical and mean field semiclassical limit from the magnetized Schrödinger-Poisson and von-Neumann equations, respectively. Local well-posedness of the underlying monokinetic PDE is also addressed. In both limits, the magnetic field is external and may be spatially non-uniform. Our results fall in the broader scope of semiclassical and quantum mean field limits for magnetized quantum dynamics.
Comments48 pages
