论文标题
多体schrödinger动力学的两粒子还原密度基质的混合符号估计值用于推导Vlasov方程
A mixed-norm estimate of the two-particle reduced density matrix of many-body Schrödinger dynamics for deriving the Vlasov equation
论文作者
论文摘要
我们使用Husimi Measure Framework重新检查了$ n $fermionicSchrödinger方程中的纯净状态初始数据，重新检查了$ n $ bodyfermionicschrödinger方程中的半古典和平均场限制。 Husimi测量方程涉及三种残基类型：动力学，半经典和平均场。本文的主要结果是比\ cite {Chen2021JSP}中的动力学和平均场残基更好地估计。特别是，通过对两粒子还原密度矩阵分解的混合 - 标记估计，对平均场残基的估计值显示为小于半经典残基。我们的分析还更新了\ cite {Chen2021JSP}中剩余项估计中的振荡估计零件。
We re-examine the combined semi-classical and mean-field limit in the $N$-body fermionic Schrödinger equation with pure state initial data using the Husimi measure framework. The Husimi measure equation involves three residue types: kinetic, semiclassical, and mean-field. The main result of this paper is to provide better estimates for the kinetic and mean-field residue than those in \cite{Chen2021JSP}. Especially, the estimate for the mean-field residue is shown to be smaller than the semiclassical residue by a mixed-norm estimate of the two-particle reduced density matrix factorization. Our analysis also updates the oscillation estimate parts in the residual term estimates appeared in \cite{Chen2021JSP}.
