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# Communications in Mathematical Sciences

## Volume 14 (2016)

### Number 4

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

Pages: 987 – 1003

DOI: http://dx.doi.org/10.4310/CMS.2016.v14.n4.a6

#### Author

#### Abstract

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.

#### Keywords

quantum theory, density functional theory, paramagnetic current, representability

#### 2010 Mathematics Subject Classification

81Q05, 81V55