Communications in Mathematical Sciences

Volume 14 (2016)

Number 4

Pure-state $N$-representability in current-spin-density functional theory

Pages: 987 – 1003



David Gontier (Université Paris Est, CERMICS (ENPC), INRIA, Marne-la-Vallée, France)


This paper is concerned with the pure-state $N$-representability problem for systems under a magnetic field. Necessary and sufficient conditions are given for a spin-density $2 times 2$ matrix $R$ to be representable by a Slater determinant. We also provide sufficient conditions on the paramagnetic current $\mathrm{j}$ for the pair $(R, \mathrm{j})$ to be Slater-representable in the case where the number of electrons $N$ is greater than $12$. The case $N \lt 12$ is left open.


quantum theory, density functional theory, paramagnetic current, representability

2010 Mathematics Subject Classification

81Q05, 81V55

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Published 6 April 2016