Systematic derivation of angular-averaged Ewald potential. (23rd September 2022)

• Record Type: Journal Article
• Authors: Demyanov, G S; Levashov, P R
• Is Part Of: Journal of physics. Volume 55:Number 38(2022)
• Publication Date: 2022-09-23
• Subjects: Ewald potential -- two-component plasma -- Euler–Maclaurin -- Poisson -- Jacobi theta function -- disordered Coulomb systems -- angular-averaged potential; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ac870b
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: In this work we provide a step by step derivation of an angular-averaged Ewald potential suitable for numerical simulations of disordered Coulomb systems. The potential was first introduced by E Yakub and C Ronchi without a clear derivation. Two methods are used to find the coefficients of the series expansion of the potential: based on the Euler–Maclaurin and Poisson summation formulas. The expressions for each coefficient is represented as a finite series containing derivatives of Jacobi theta functions. We also demonstrate the formal equivalence of the Poisson and Euler–Maclaurin summation formulas in the three-dimensional case. The effectiveness of the angular-averaged Ewald potential is shown by the example of calculating the Madelung constant for a number of crystal lattices.