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- W1967171242 abstract "We consider the v-representability of the particle density for a noninteracting system of spinless fermions by introducing the idea of proper order of a set of energy levels. It is shown that if ${mathit{E}}_{1}$(ensuremath{lambda}), ${mathit{E}}_{2}$(ensuremath{lambda}), and ${mathit{E}}_{3}$(ensuremath{lambda}) are three energy levels associated with some local potential ${mathit{V}}_{ensuremath{lambda}}$(r) that is a continuous function of ensuremath{lambda}=(${ensuremath{lambda}}_{1}$,${ensuremath{lambda}}_{2}$,${ensuremath{lambda}}_{3}$) over all possible points ensuremath{lambda}, where ${ensuremath{lambda}}_{mathit{i}}$ is the occupation number of the ith state and M=${ensuremath{lambda}}_{1}$+${ensuremath{lambda}}_{2}$+${ensuremath{lambda}}_{3}$ is the total number of particles distributed over the three levels, then there must be at least one ensuremath{lambda} for which the three levels are in so-called proper order, in which the levels below the highest occupied level are filled. This result provides a basis for the proof of ensemble v-representability of some N-particle density for which the ground-state degeneracy of the system is no more than three. As examples, three- and two-dimensional central systems are examined, and an N-particle central density is shown to be ensemble v-representable for small N (Nensuremath{le}14 and Nensuremath{le}9 for three- and two-dimensional cases, respectively). The implications for density-functional theory are discussed." @default.
- W1967171242 created "2016-06-24" @default.
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- W1967171242 date "1991-09-01" @default.
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- W1967171242 title "<i>v</i>-representability for systems with low degeneracy" @default.
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- W1967171242 doi "https://doi.org/10.1103/physreva.44.2816" @default.
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