Defect-free global minima in Thomson's problem of charges on a sphere.
Given unit points charges on the surface of a unit conducting sphere, what configuration of charges minimizes the Coulombic energy SigmaN i>(j=1)1/r(ij)? Due to an exponential rise in good local minima, finding global minima for this problem, or even approaches to do so has proven extremely difficult. For N=10(h2+hk+k2)+2 recent theoretical work based on elasticity theory, and subsequent numerical work has shown, that for N approximately same or greater than 500-1000, adding dislocation defects to a symmetric icosadeltahedral lattice lowers the energy. Here we show that in fact this approach holds for all N, and we give a complete or near complete catalogue of defect free global minima.
Altschuler
Eric Lewin
EL
Department of Physical Medicine and Rehabilitation, University of Medicine and Dentistry of New Jersey, 30 Bergen Street, ADMC 1, Suite 101 Newark, NJ 07101, USA. eric.altschuler@umdnj.edu
Pérez-Garrido
Antonio
A