Fourier expansions for the potentials of lattices of charge

TL;DR

This paper derives explicit Fourier series expressions for lattice potentials with generalized charges, including Coulomb and Yukawa interactions, and explores their applications to finite and disordered lattices.

Contribution

It provides a systematic method to compute Fourier coefficients of lattice potentials for various charge distributions using the Poisson sum rule.

Findings

Explicit Fourier coefficients for Coulomb and Yukawa potentials are derived.

The approach extends to finite and disordered lattice configurations.

Formal expressions facilitate analysis of lattice potentials in different contexts.

Abstract

We apply the Poisson sum rule to obtain formal expressions for the Fourier coefficients of the potential of a lattice of generalized charge. Each generalized charge is assumed to contribute to the potential a term which depends only on the vector displacement from the charge's location. The coefficients are explicitly calculated for Coulomb and Yukawa-type individual particle potentials. The potentials of finite and disordered lattices are also briefly considered.