论文标题
TFDW能量与液滴模型的收敛
Convergence of the TFDW Energy to the Liquid Drop Model
论文作者
论文摘要
我们考虑了在物理环境中产生的两个非局部变异模型。第一个是Thomas-Fermi-Dirac-vonWeizäcker（TFDW）模型，在原子和分子的电离研究中引入，第二个是具有外部潜力的液态液滴模型，Gamow在核结构的背景下提出。已经观察到，这两个模型具有许多相同的特性，尤其是在最小化器的存在和不存在方面。我们表明，在一般的外部电势类别中，在系数和约束质量的“尖锐界面”缩放下，TFDW能量伽马置换到液滴模型。最后，我们对每个模型的全球最小化产生了一些后果。
We consider two nonlocal variational models arising in physical contexts. The first is the Thomas-Fermi-Dirac-von Weizäcker (TFDW) model, introduced in the study of ionization of atoms and molecules, and the second is the liquid drop model with external potential, proposed by Gamow in the context of nuclear structure. It has been observed that the two models exhibit many of the same properties, especially in regard to the existence and nonexistence of minimizers. We show that, under a "sharp interface" scaling of the coefficients and constrained mass, the TFDW energy Gamma-converges to the Liquid Drop model, for a general class of external potentials. Finally, we present some consequences for global minimization of each model.
