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Kohn-Sham Theory in the Presence of Magnetic Field

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Andre Laestadius

Mathematical Physics · Submitted 11 Apr 2014

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Since a Levy-Lieb-type functional can be defined for Current Density Functional Theory formulated with the paramagnetic current density, we here develop a rigorous $N$-representable Kohn-Sham approach for interacting electrons in magnetic field.

how it is stated · asserted 1.00 read the record →

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arXiv ID1404.3098 (version 1)
Pith ID5WF5H4ZX, Pith's permanent record of this paper and its review
CitationAndre Laestadius. "Kohn-Sham Theory in the Presence of Magnetic Field." arXiv:1404.3098 (2014). https://pith.science/paper/5WF5H4ZX
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,508 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.13 · states limitation 0.18 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.70 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In the well-known Kohn-Sham theory in Density Functional Theory, a fictitious non-interacting system is introduced that has the same particle density as a system of $N$ electrons subjected to mutual Coulomb repulsion and an external electric field. For a long time, the treatment of the kinetic energy was not correct and the theory was not well-defined for $N$-representable particle densities. In the work of [Hadjisavvas and Theophilou, Phys. Rev. A, 1984, 30, 2183], a rigorous Kohn-Sham theory for $N$-representable particle densities was developed using the Levy-Lieb functional. Since a Levy-Lieb-type functional can be defined for Current Density Functional Theory formulated with the paramagnetic current density, we here develop a rigorous $N$-representable Kohn-Sham approach for interacting electrons in magnetic field. Furthermore, in the one-electron case, criteria for $N$-representable particle densities to be $v$-representable are given.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In the well-known Kohn-Sham theory in Density Functional Theory, a fictitious non-interacting system is introduced that has the same particle density as a system of $N$ electrons subjected to mutual Coulomb repulsion and an external electric field. background 1.00 0.04 0.03 asserted 1.00
s1 For a long time, the treatment of the kinetic energy was not correct and the theory was not well-defined for $N$-representable particle densities. gap 0.86 0.05 0.02 asserted 1.00
s2 In the work of [Hadjisavvas and Theophilou, Phys. Rev. A, 1984, 30, 2183], a rigorous Kohn-Sham theory for $N$-representable particle densities was developed using the Levy-Lieb functional. background 0.98 0.03 0.07 asserted 1.00
s3 Since a Levy-Lieb-type functional can be defined for Current Density Functional Theory formulated with the paramagnetic current density, we here develop a rigorous $N$-representable Kohn-Sham approach for interacting electrons in magnetic field. contribution 1.00 0.92 0.76 asserted 1.00
s4 Furthermore, in the one-electron case, criteria for $N$-representable particle densities to be $v$-representable are given. result 0.59 0.85 0.12 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.84 · evidence from proof or derivation 0.97.

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  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In the well-known Kohn-Sham theory in Density Functional Theory, a fictitious non-interacting system is introduced that has the same particle density as a system of $N$ electrons subjected to mutual Coulomb repulsion and an external electric field. For a long time, the treatment of the kinetic energy was not correct and the theory was not well-defined for $N$-representable particle densities. In the work of [Hadjisavvas and Theophilou, Phys. Rev. A, 1984, 30, 2183], a rigorous Kohn-Sham theory for $N$-representable particle densities was developed using the Levy-Lieb functional. Since a Levy-Lieb-type functional can be defined for Current Density Functional Theory formulated with the paramagnetic current density, we here develop a rigorous $N$-representable Kohn-Sham approach for interacting electrons in magnetic field. Furthermore, in the one-electron case, criteria for $N$-representable particle densities to be $v$-representable are given.

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