费米海中薄片状缺陷的简化Hartree-Fock模型
A reduced Hartree-Fock model of slice-like defects in the Fermi sea
摘要：
研究材料中缺陷的电子结构是凝聚态物理的重要课题。从数学的角度来看，绝缘体中局部缺陷的非线性平均场模型是很好理解的。我们在这里提出了一个平均场模型来研究金属中扩展缺陷的一个特殊例子。这些扩展的缺陷通常对应于在三维均匀电子气中取出有限宽度的板。我们工作的框架内减少Hartree-Fock模型与汤川或库仑相互作用。利用~[Frank 2011，Frank 2013]中发展的方法研究了自由电子气的局域扰动，证明了我们的模型存在极小值，并且当Yukawa参数趋于零时，Yukawa基态能量和密度矩阵收敛到基态库仑能量和密度矩阵.此外，我们提出了数值模拟，我们观察到弗里德尔振荡的总电子密度。
英文摘要：
Studying the electronic structure of defects in materials is an important subject in condensed matter physics. From a mathematical point of view, nonlinear mean-field models of localized defects in insulators are well understood. We present here a mean-field model to study a particular instance of extended defects in metals. These extended defects typically correspond to taking out a slab of finite width in the three-dimensional homogeneous electron gas. We work in the framework of the reduced Hartree-Fock model with either Yukawa or Coulomb interactions. Using techniques developed in~[Frank2011, Frank2013] to study local perturbations of the free-electron gas, we show that our model admits minimizers, and that Yukawa ground state energies and density matrices converge to ground state Coulomb energies and density matrices as the Yukawa parameter tends to zero. We moreover present numerical simulations where we observe Friedel oscillations in the total electronic density.
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