标题： 广义托马斯-费米-魏茨萨克泛函的过量电荷界限 显示英文标题

标题： Bound on the Excess Charge of Generalized Thomas-Fermi-Weizsäcker Functionals

摘要： 我们限制了原子在超出电中性的情况下可以结合的电子数$Q$，对于推广经典 Thomas-Fermi-Weizsäcker 泛函的密度泛函：除了经典的幂$5/3$，还考虑了更一般的幂$p$。对于$3/2<p<2$我们证明了过剩电荷猜想，即$Q$在原子序数$Z$中是均匀有界的。 情况$p=3/2$是关键的：行为从在$Z$中的均匀界变为非线性项临界耦合$4\sqrt\pi$处的线性界。 我们还改进了所有$p\geq6/5$的线性界。 显示英文摘要

摘要： We bound the number of electrons $Q$ that an atom can bind in excess of neutrality for density functionals generalizing the classical Thomas-Fermi-Weizs\"acker functional: instead of the classical power $5/3$ more general powers $p$ are considered. For $3/2<p<2$ we prove the excess charge conjecture, i.e., that $Q$ is uniformly bounded in the atomic number $Z$. The case $p=3/2$ is critical: the behavior changes from a uniform bound in $Z$ to a linear bound at the critical coupling $4\sqrt\pi$ of the nonlinear term. We also improve the linear bound for all $p\geq6/5$.