论文标题
关于时间依赖的Hartree-fock方程的推导的两条评论
Two Comments on the Derivation of the Time-Dependent Hartree-Fock Equation
论文作者
论文摘要
我们重新审视了时间依赖性的Hartree方程的推导，以在耦合均值场和半经典缩放的政权中相互作用，从而对Benedikter，Porta和Schlein在2014年获得的结果贡献了两个评论。首先，该派生在任意空间维度中。其次，通过使用明确的公式进行粒子孔转换的单位实施，我们以类似于玻色子的Rodnianski和Schlein的连贯状态方法的形式进行了证明。
We revisit the derivation of the time-dependent Hartree-Fock equation for interacting fermions in a regime coupling a mean-field and a semiclassical scaling, contributing two comments to the result obtained in 2014 by Benedikter, Porta, and Schlein. First, the derivation holds in arbitrary space dimension. Second, by using an explicit formula for the unitary implementation of particle-hole transformations, we cast the proof in a form similar to the coherent state method of Rodnianski and Schlein for bosons.
