论文标题
Hartree和Hartree-fock到Vlasov-Poisson方程的强大半经典极限
Strong semiclassical limit from Hartree and Hartree-Fock to Vlasov-Poisson equation
论文作者
论文摘要
我们考虑从哈特里到弗拉索夫方程的半经典极限，具有一般的奇异相互作用势，包括库仑和重力相互作用，我们证明了Schatten规范强的拓扑中的明确界限。此外，在费米子的情况下，我们提供了关于Hartree-fock方程中交换项的大小的估计值，并且还获得了从Hartree-fock到Schatten Norms中Vlasov方程的半经典限制的收敛速率。我们的结果适用于某些Sobolev空间和任何固定时间间隔的一般初始数据。
We consider the semiclassical limit from the Hartree to the Vlasov equation with general singular interaction potential including the Coulomb and gravitational interactions, and we prove explicit bounds in the strong topologies of Schatten norms. Moreover, in the case of fermions, we provide estimates on the size of the exchange term in the Hartree-Fock equation and also obtain a rate of convergence for the semiclassical limit from the Hartree-Fock to the Vlasov equation in Schatten norms. Our results hold for general initial data in some Sobolev space and any fixed time interval.
