具有奇异相互作用的费米子的平均场演化
Mean-field evolution of fermions with singular interaction
摘要：
本文考虑了N个费米子在平均场区通过反幂律势$V(x)=1/|x|^α$相互作用的系统，其中$α\in(0,1]$。证明了多体薛定谔方程的解在约化密度矩阵意义下收敛于含时Hartree-Fock方程的解.我们强调依赖于奇异性的潜力的规则性的初始数据。证明是[22]的改编，其中处理了$α=1$的情况。
英文摘要：
We consider a system of N fermions in the mean-field regime interacting though an inverse power law potential $V(x)=1/|x|^α$, for $α\in(0,1]$. We prove the convergence of a solution of the many-body Schrödinger equation to a solution of the time-dependent Hartree-Fock equation in the sense of reduced density matrices. We stress the dependence on the singularity of the potential in the regularity of the initial data. The proof is an adaptation of [22], where the case $α=1$ is treated.
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