New global minima for Thomson´s problem of charges on a sphere
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Área de conocimientoFísica Aplicada
PatrocinadoresWe 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.
Fecha de publicación2005-04
EditorialAmerican Physical Society
Cita bibliográficaALTSCHULER, 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
Palabras claveProblema 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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