preprint · arXiv (Cornell University) · 2018

Density-Wavefunction Mapping in Degenerate Current-Density-Functional Theory

Laestadius, Andre, Tellgren, Erik I.

Cited by 0Open access

Abstract

We show that the particle density, $ρ(\mathbf{r})$, and the paramagnetic current density, $\mathbf{j}^{p}(\mathbf{r})$, are not sufficient to determine the set of degenerate ground-state wave functions. This is a general feature of degenerate systems where the degenerate states have different angular momenta. We provide a general strategy for constructing Hamiltonians that share the same ground state density, yet differ in degree of degeneracy. We then provide a fully analytical example for a noninteracting system subject to electrostatic potentials and uniform magnetic fields. Moreover, we prove that when $(ρ,\mathbf{j}^p)$ is ensemble $(v,\mathbf{A})$-representable by a mixed state formed from $r$ degenerate ground states, then any Hamiltonian $H(v',\mathbf{A}')$ that shares this ground state density pair must have at least $r$ degenerate ground states in common with $H(v,\mathbf{A})$. Thus, any set of Hamiltonians that shares a ground-state density pair $(ρ,\mathbf{j}^p)$ by necessity has at least have one joint ground state.

Cite this paper

APA 7

Laestadius, A., & Tellgren, E. I. (2018). Density-Wavefunction Mapping in Degenerate Current-Density-Functional Theory. arXiv (Cornell University). https://doi.org/10.48550/arxiv.1801.09606

MLA 9

Laestadius, Andre, and Erik I. Tellgren. “Density-Wavefunction Mapping in Degenerate Current-Density-Functional Theory.” arXiv (Cornell University), 2018, https://doi.org/10.48550/arxiv.1801.09606.

Chicago

Laestadius, Andre, and Erik I. Tellgren. 2018. “Density-Wavefunction Mapping in Degenerate Current-Density-Functional Theory.” arXiv (Cornell University). https://doi.org/10.48550/arxiv.1801.09606.

Harvard

Laestadius, A. and Tellgren, E.I. (2018) ‘Density-Wavefunction Mapping in Degenerate Current-Density-Functional Theory’, arXiv (Cornell University). Available at: https://doi.org/10.48550/arxiv.1801.09606.

BibTeX

@misc{laestadius2018density,
  title = {{Density-Wavefunction Mapping in Degenerate Current-Density-Functional Theory}},
  author = {Laestadius, Andre and Tellgren, Erik I.},
  journal = {arXiv (Cornell University)},
  year = {2018},
  doi = {10.48550/arxiv.1801.09606}
}

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