On Born’s Conjecture about Optimal Distribution of Charges for an Infinite Ionic Crystal

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Standard

On Born’s Conjecture about Optimal Distribution of Charges for an Infinite Ionic Crystal. / Bétermin, Laurent; Knüpfer, Hans.

I: Journal of Nonlinear Science, Bind 28, Nr. 5, 16.04.2018, s. 1629–1656 .

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Bétermin, L & Knüpfer, H 2018, 'On Born’s Conjecture about Optimal Distribution of Charges for an Infinite Ionic Crystal', Journal of Nonlinear Science, bind 28, nr. 5, s. 1629–1656 . https://doi.org/10.1007/s00332-018-9460-3

APA

Bétermin, L., & Knüpfer, H. (2018). On Born’s Conjecture about Optimal Distribution of Charges for an Infinite Ionic Crystal. Journal of Nonlinear Science, 28(5), 1629–1656 . https://doi.org/10.1007/s00332-018-9460-3

Vancouver

Bétermin L, Knüpfer H. On Born’s Conjecture about Optimal Distribution of Charges for an Infinite Ionic Crystal. Journal of Nonlinear Science. 2018 apr. 16;28(5):1629–1656 . https://doi.org/10.1007/s00332-018-9460-3

Author

Bétermin, Laurent ; Knüpfer, Hans. / On Born’s Conjecture about Optimal Distribution of Charges for an Infinite Ionic Crystal. I: Journal of Nonlinear Science. 2018 ; Bind 28, Nr. 5. s. 1629–1656 .

Bibtex

@article{9a4da722eabb4a5e80c328a9d8e1182a,
title = "On Born{\textquoteright}s Conjecture about Optimal Distribution of Charges for an Infinite Ionic Crystal",
abstract = "We study the problem for the optimal charge distribution on the sites of a fixed Bravais lattice. In particular, we prove Born{\textquoteright}s conjecture about the optimality of the rock salt alternate distribution of charges on a cubic lattice (and more generally on a d-dimensional orthorhombic lattice). Furthermore, we study this problem on the two-dimensional triangular lattice and we prove the optimality of a two-component honeycomb distribution of charges. The results hold for a class of completely monotone interaction potentials which includes Coulomb-type interactions for d≥3. In a more general setting, we derive a connection between the optimal charge problem and a minimization problem for the translated lattice theta function.",
author = "Laurent B{\'e}termin and Hans Kn{\"u}pfer",
year = "2018",
month = apr,
day = "16",
doi = "10.1007/s00332-018-9460-3",
language = "English",
volume = "28",
pages = "1629–1656 ",
journal = "Journal of Nonlinear Science",
issn = "0938-8974",
publisher = "Springer",
number = "5",

}

RIS

TY - JOUR

T1 - On Born’s Conjecture about Optimal Distribution of Charges for an Infinite Ionic Crystal

AU - Bétermin, Laurent

AU - Knüpfer, Hans

PY - 2018/4/16

Y1 - 2018/4/16

N2 - We study the problem for the optimal charge distribution on the sites of a fixed Bravais lattice. In particular, we prove Born’s conjecture about the optimality of the rock salt alternate distribution of charges on a cubic lattice (and more generally on a d-dimensional orthorhombic lattice). Furthermore, we study this problem on the two-dimensional triangular lattice and we prove the optimality of a two-component honeycomb distribution of charges. The results hold for a class of completely monotone interaction potentials which includes Coulomb-type interactions for d≥3. In a more general setting, we derive a connection between the optimal charge problem and a minimization problem for the translated lattice theta function.

AB - We study the problem for the optimal charge distribution on the sites of a fixed Bravais lattice. In particular, we prove Born’s conjecture about the optimality of the rock salt alternate distribution of charges on a cubic lattice (and more generally on a d-dimensional orthorhombic lattice). Furthermore, we study this problem on the two-dimensional triangular lattice and we prove the optimality of a two-component honeycomb distribution of charges. The results hold for a class of completely monotone interaction potentials which includes Coulomb-type interactions for d≥3. In a more general setting, we derive a connection between the optimal charge problem and a minimization problem for the translated lattice theta function.

U2 - 10.1007/s00332-018-9460-3

DO - 10.1007/s00332-018-9460-3

M3 - Journal article

VL - 28

SP - 1629

EP - 1656

JO - Journal of Nonlinear Science

JF - Journal of Nonlinear Science

SN - 0938-8974

IS - 5

ER -

ID: 195196639