论文标题
磁性liouville方程式为半古典极限
The magnetic Liouville equation as a semi-classical limit
论文作者
论文摘要
具有非恒定磁场的liouville方程是在具有相同磁场的海森伯格方程的普朗克常数\ hbar中获得的。收敛性相对于适当的半古典伪距离，因此相对于Monge-Kantorovich距离。对于表格\ frac {1}εx^{\ bot}的特定2D情况，证明了ε和\ hbar中的均匀估计。作为应用，获得了具有磁性矢量电势的海森堡方程的观察不等式。这些结果分别是作品[7]和[8]的磁性变体。
The Liouville equation with non-constant magnetic field is obtained as a limit in the Planck constant \hbar of the Heisenberg equation with the same magnetic field. The convergence is with respect to an appropriate semi-classical pseudo distance, and consequently with respect to the Monge-Kantorovich distance. Uniform estimates both in εand \hbar are proved for the specific 2D case of a magnetic vector potential of the form \frac {1} εx^{\bot}. As an application, an observation inequality for the Heisenberg equation with a magnetic vector potential is obtained. These results are a magnetic variant of the works [7] and [8] respectively.
