Evaluation of lattice sums using Poisson's summation formula. II

Abstract

For pt.I see J. Math. Phys., vol.16, p.1457 of 1975. Application of Poisson's summation formula for the analytic evaluation of a class of lattice sums in arbitrary dimensions is extended to a more generalized class of sums. The resulting formulae are applicable to a variety of problems such as electronic-structure studies of crystalline solids, the onset of Bose-Einstein condensation in finite systems, the analysis of stability of quantized vortex arrays in extreme type-II superconductors and in rotating superfluid helium, plasma oscillations in an array of filamentary conductors, etc. They also provide an alternative approach for the determination of Madelung constants and other related sums that appear in the theory of cubic lattices.