期刊
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
卷 47, 期 2, 页码 1001-1021出版社
SIAM PUBLICATIONS
DOI: 10.1137/130949932
关键词
crystal; lattice; ion; charge; wave function; potential; Schrodinger equation; Poisson equation; elementary cell; energy; Coulomb energy; minimization; neutrality condition; spectrum; embedding theorems; Fourier transform; infrared divergence; variation; nanostructures
资金
- Alexander von Humboldt Research Award
- Austrian Science Fund [P22198-N13]
- DFG
- Russian Foundation for Basic Research
- Austrian Science Fund (FWF) [P 22198] Funding Source: researchfish
- Austrian Science Fund (FWF) [P22198] Funding Source: Austrian Science Fund (FWF)
A space-periodic ground state is shown to exist for lattices of smeared ions in R-3 coupled to the Schrodinger and scalar fields. The elementary cell is necessarily neutral. The one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) lattices in R-3 are considered, and a ground state is constructed by minimizing the energy per cell. The case of a 3D lattice is rather standard, because the elementary cell is compact, and the spectrum of the Laplacian is discrete. In the cases of 1D and 2D lattices, the energy functional is differentiable only on a dense set of variations, due to the presence of the continuous spectrum of the Laplacian that causes the infrared divergence of the Coulomb bond. Respectively, the construction of electrostatic potential and the derivation of the Schrodinger equation for the minimizer in these cases require an extra argument. The space-periodic ground states for 1D and 2D lattices give the model of the nanostructures similar to the carbon nanotubes and graphene, respectively.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据