Abstract
We attack the generalized Thomson problem, i.e., determining the ground state energy and configuration of many particles interacting via an arbitrary repulsive pairwise potential on a sphere via a continuum mapping onto a universal long range interaction between angular disclination defects parametrized by the elastic (Young) modulus Y of the underlying lattice and the core energy E(core) of an isolated disclination. Predictions from the continuum theory for the ground state energy agree with numerical simulations of long range power law interactions of the form 1/r(gamma) (0<gamma<2) to four significant figures. The generality of our approach is illustrated by a study of grain boundary proliferation for tilted crystalline order and square lattices on the sphere.
Highlights
We attack generalized Thomson problems with a continuum formalism which exploits a universal long range interaction between defects depending on the Young modulus of the underlying lattice
The Thomson problem of constructing the ground state of electrons interacting with a repulsive Coulomb potential on a 2-sphere [1] is almost one hundred years old [2] and has many important physical realizations
The original Thomson problem refers to the ground state of spherical shells of electrons, one can ask for crystalline ground states of particles interacting with other potentials
Summary
We attack generalized Thomson problems with a continuum formalism which exploits a universal long range interaction between defects depending on the Young modulus of the underlying lattice. The Thomson problem of constructing the ground state of (classical) electrons interacting with a repulsive Coulomb potential on a 2-sphere [1] is almost one hundred years old [2] and has many important physical realizations.
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