Current densities in density-functional theory
Current densities in density-functional theory
复制标题
密度泛函理论中的电流密度
DOI：
10.1103/physreva.88.032516
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发表时间：
2013
影响因子：
2.9
通讯作者：
R. Schrader
中科院分区：
文献类型：
--
作者：
E. Lieb;R. Schrader
众所周知，任何给定的密度ρ（x）都可以由N个粒子的行列式波函数来实现。这里要解决的问题是，任何给定的密度ρ（x）和电流密度j（x）是否可以同时由（有限动能）行列式波函数实现。在速度场v（x）=j（x）/rho（x）无旋度的情况下，我们给出了所有N的解，并给出了能量的显式上界。如果速度场不是旋度自由的，则对于所有N\geq 4都存在有限能量解，但在这种情况下我们没有提供明确的能量界。对于N=2，我们提供了一个有解的非旋度自由速度场的例子，以及一个没有解的例子。对于N=3且无旋度速度场的情况，则不作讨论.
It is well known that any given density rho(x)can be realized by a determinantal wave function for N particles. The question addressed here is whether any given density rho(x) and current density j(x) can be simultaneously realized by a (finite kinetic energy) determinantal wave function. In case the velocity field v(x) =j(x)/rho(x) is curl free, we provide a solution for all N, and we provide an explicit upper bound for the energy. If the velocity field is not curl free, there is a finite energy solution for all N\geq 4, but we do not provide an explicit energy bound in this case. For N=2 we provide an example of a non curl free velocity field for which there is a solution, and an example for which there is no solution. The case $N=3 with a non curl free velocity field is left open.