On Born’s Conjecture about Optimal Distribution of Charges for an Infinite Ionic Crystal
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- Born Conjecture BETERMIN KNUEPFER
Accepted author manuscript, 366 KB, PDF document
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.
Original language | English |
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Journal | Journal of Nonlinear Science |
Volume | 28 |
Issue number | 5 |
Pages (from-to) | 1629–1656 |
ISSN | 0938-8974 |
DOIs | |
Publication status | Published - 16 Apr 2018 |
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