Abstract
A variational property of the ground-state energy of an electron gas in an external potential $v(\mathrm{r})$, derived by Hohenberg and Kohn, is extended to nonzero temperatures. It is first shown that in the grand canonical ensemble at a given temperature and chemical potential, no two $v(\mathrm{r})$ lead to the same equilibrium density. This fact enables one to define a functional of the density $F[n(\mathrm{r})]$ independent of $v(\mathrm{r})$, such that the quantity $\ensuremath{\Omega}=\ensuremath{\int}v(\mathrm{r})n(\mathrm{r})d\mathrm{r}+F[n(\mathrm{r})]$ is at a minimum and equal to the grand potential when $n(\mathrm{r})$ is the equilibrium density in the grand ensemble in the presence of $v(\mathrm{r})$.
Keywords
PhysicsGrand canonical ensembleOmegaFermi gasEnergy (signal processing)Ground stateGrand potentialElectronAtomic physicsThermodynamicsQuantum mechanicsMathematicsStatistics
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Publication Info
- Year
- 1965
- Type
- article
- Volume
- 137
- Issue
- 5A
- Pages
- A1441-A1443
- Citations
- 2701
- Access
- Closed
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Cite This
N. David Mermin
(1965).
Thermal Properties of the Inhomogeneous Electron Gas.
Physical Review
, 137
(5A)
, A1441-A1443.
https://doi.org/10.1103/physrev.137.a1441
Identifiers
- DOI
- 10.1103/physrev.137.a1441