Oscillatory and fluctuating terms in energies of assemblies of equicharged particles subject to spherically symmetric power-law confining potentials

摘要

Energies E(N) of assemblies of equicharged particles subject to spherically symmetric power-law confining potentials vary in a convoluted fashion with the particle totalities N. Accurate rigorous upper bounds to these energies, which are amenable to detailed mathematical analysis, are found to comprise terms with smooth, oscillatory, and fluctuating dependences on N. The smooth energy component is obtained as a power series in N~(-2/3) with the first two terms corresponding to the bulk and Madelung energies. The oscillatory component possesses the large-N asymptotics given by a product of N ~(1/(λ + 1)), where λ is the power-law exponent, and a function periodic in N~(1/3). The amplitude of the fluctuating component, which originates mostly from the irregular dependence of the Thomson energy ETh(n) on n, also scales like N~(1/(λ + 1)).