Equality of the Jellium and Uniform Electron Gas next-order asymptotic terms for Riesz potentials
Equality of the Jellium and Uniform Electron Gas next-order asymptotic terms for Riesz potentials
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Jellium 和均匀电子气 Riesz 势的下阶渐近项的等式
DOI：
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发表时间：
2017
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通讯作者：
Mircea Petrache
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作者：
Codina Cotar;Mircea Petrache
我们考虑两个尖锐的次阶渐近问题，即最优点配置的最小能量的渐近性和多边缘最优运输的渐近性，在这两种情况下，Riesz成本与逆幂律长程相互作用。第一个问题描述了库仑或Riesz气体的基态，而第二个出现作为半经典极限的密度泛函理论能量建模的量子版本的相同的系统。最近，在这些扩展中的二阶项被精确地描述，并分别对应于一个Jeltron和一个均匀电子气模型。目前的工作表明，逆幂律相互作用的功率$sin]d-2，d[$在$d$维，这两个问题有相同的最小值。我们还表明，在整个范围$sin]0，d[$的均匀电子气的最佳常数是连续的$s$。
We consider two sharp next order asymptotics problems, namely the asymptotics for the minimum energy for optimal point configurations and the asymptotics for the many-marginals Optimal Transport, in both cases with Riesz costs with inverse power-law long range interactions. The first problem describes the ground state of a Coulomb or Riesz gas, while the second appears as a semiclassical limit of the Density Functional Theory energy modelling a quantum version of the same system. Recently the second-order term in these expansions was precisely described, and corresponds respectively to a Jellium and to a Uniform Electron Gas model. The present work shows that for inverse-power-law interactions with power $sin]d-2,d[$ in $d$ dimensions, the two problems have the same minimum. We also show that on the whole range $sin]0,d[$ the Uniform Electron Gas optimal constant is continuous in $s$.