Ewald method for polytropic potentials in arbitrary dimensionality

Details Ewald method for polytropic potentials in arbitrary dimensionality Ewald method for polytropic potentials in arbitrary dimensionality

2011-07-27

arxiv.org/abs/1107.5435v1

Physics

Condensed Matter

Quantum Gases

41 pages, 3 figures

Scientific paper

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.

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