论文标题
在空间均匀的量子玻尔兹曼方程的半古典极限上：弱收敛性
On semi-classical limit of spatially homogeneous quantum Boltzmann equation: weak convergence
论文作者
论文摘要
在物理学中可以预期，具有费米 - 迪拉克或Bose-Einstein统计的同质量子螺栓骨架以及Maxwell-Boltzmann操作员（统计效果）对弱耦合气体的忽略将收敛到同质fokker-planck-landaue equarion $ $ $ \ hbar y \ hbar the planck comvants $ \ hbar。在本文和即将到来的工作\ cite {hlp2}中，我们将在此半古典限制上提供数学上的理由。证明的关键要素是捕获{\ IT弱投影梯度}的新框架，这是由Villani \ Cite \ Cite {V1}激励的，以识别Fokker-Planck-Landau方程的$ H $ - 解决方案，以及在碰撞运营商的立方体中的对称结构。
It is expected in physics that the homogeneous quantum Boltzmann equation with Fermi-Dirac or Bose-Einstein statistics and with Maxwell-Boltzmann operator (neglecting effect of the statistics) for the weak coupled gases will converge to the homogeneous Fokker-Planck-Landau equation as the Planck constant $\hbar$ tends to zero. In this paper and the upcoming work \cite{HLP2}, we will provide a mathematical justification on this semi-classical limit. Key ingredients into the proofs are the new framework to catch the {\it weak projection gradient}, which is motivated by Villani \cite{V1} to identify the $H$-solution for Fokker-Planck-Landau equation, and the symmetric structure inside the cubic terms of the collision operators.
