Ewald method for polytropic potentials in arbitrary dimensionality

Abstract

The Ewald summation technique is generalised to power-law 1/|r|^k potentials in three-, two- and one-dimensional geometries with explicit formulae for all the components of the sums. The cases of short-range, long-range and "marginal" interactions are treated separately. The jellium model, as a particular case of a charge-neutral system, is discussed and the explicit forms of the Ewald sums for such system are presented. A generalised form of the Ewald sums for a noncubic (nonsquare) simulation cell for three- (two-) dimensional geometry is obtained and its possible field of application is discussed. A procedure for the optimisation of the involved parameters in actual simulations is developed and an example of its application is presented.

41 pages, 3 figures

References in corpus (2)

• Quantum melting of a crystal of dipolar bosons
• Structure and melting behavior of classical bilayer crystals of dipoles

Cited by in corpus (5)

• Periodic Discrete Energy for Long-Range Potentials
• On Born's conjecture about optimal distribution of charges for an infinite ionic crystal
• Zero-temperature phase diagram of Yukawa bosons
• Composite boson description of a low density gas of excitons
• The inverse-square interaction phase diagram: unitarity in the bosonic ground state