Coarse-grained V-representability

Details Coarse-grained V-representability Coarse-grained V-representability

2007-02-13

arxiv.org/abs/cond-mat/0702291v1

J. Chem. Phys. 125, 074114 (2006)

Physics

Condensed Matter

Other Condensed Matter

10 pages, no figures, revtex4. J Chem Phys official version at http://link.aip.org/link/?jcp/125/074114

Scientific paper

10.1063/1.2336211

The unsolved problem of determining which densities are ground state densities of an interacting electron system in some external potential is important to the foundations of density functional theory. A coarse-grained version of this ensemble V-representability problem is shown to be thoroughly tractable. Averaging the density of an interacting electron system over the cells of a regular partition of space produces a coarse-grained density. It is proved that every strictly positive coarse-grained density is coarse-grained ensemble V-representable: there is a unique potential, constant over each cell of the partition, which has a ground state with the prescribed coarse-grained density. For a system confined to a box, the (coarse-grained) Lieb [Intl. J. Quantum Chem. 24, 243 (1983)] functional is also shown to be Gateaux differentiable. All results extend to open systems.

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