New global minima for Thomson´s problem of charges on a sphere
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Knowledge AreaFísica Aplicada
SponsorsWe thank the anonymous reviewers for comments extremely helpful in revising the manuscript and also inspirational leading to finding a new possible global minimum. A.P.G. would like to aknowledge financial support from Spanish MCyT under grant No. MAT2003– 04887.
PublisherAmerican Physical Society
Bibliographic CitationALTSCHULER, ERIC LEWIN., PÉREZ GARRIDO, ANTONIO. New global minima for Thomson´s problem of charges on a sphere. Physical Review E, 71 (4): 1-12, 2005. ISSN 1550-2376
KeywordsProblema de Thomson
Using numerical arguments we find that for N = 306 a tetrahedral configuration (Th) and for N = 542 a dihedral configuration (D5) are likely the global energy minimum for Thomson’s problem of minimizing the energy of N unit charges on the surface of a unit conducting sphere. These would be the largest N by far, outside of the icosadeltahedral series, for which a global minimum for Thomson’s problem is known. We also note that the current theoretical understanding of Thomson’s problem does not rule out a symmetric configuration as the global minima for N = 306 and 542. We explicitly find that analogues of the tetrahedral and dihedral configurations for N larger than 306 and 542, respectively, are not global minima, thus helping to confirm the theory of Dodgson and Moore (Phys. Rev. B 55, 3816 (1997)) that as N grows dislocation defects can lower the lattice strain of symmetric configurations and concomitantly the energy. As well, making explicit previous work by ourselves and others, ...
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