论文标题
Gell-Mann $ - $ BRUECKNER公式用于电子气的相关能量：平均场政权中严格的上限
The Gell-Mann$-$Brueckner Formula for the Correlation Energy of the Electron Gas: A Rigorous Upper Bound in the Mean-Field Regime
论文作者
论文摘要
我们证明，在平均场状态中相互作用的相互作用的相关能量对广泛的相互作用电位的相互作用能量。我们的结果涵盖了库仑电位，在这种情况下，我们获得了Gell-Mann $ -Brueckner公式的类似物$ C_ {1}ρ\ log \ left（ρ\右）+c_ {2}ρ$在高密度限制中。我们通过完善对琼脂化方法的分析来处理奇异潜力，并捕获纯粹的玻色粒图片中没有的交换贡献。
We prove a rigorous upper bound on the correlation energy of interacting fermions in the mean-field regime for a wide class of interaction potentials. Our result covers the Coulomb potential, and in this case we obtain the analogue of the Gell-Mann$-$Brueckner formula $c_{1}ρ\log\left(ρ\right)+c_{2}ρ$ in the high density limit. We do this by refining the analysis of our bosonization method to deal with singular potentials, and to capture the exchange contribution which is absent in the purely bosonic picture.
