Paper Info
Title
The Electrostatic Potential Of Periodic Crystals
Abstract
The electrostatic potentials phi associated with neutral periodic crystals are defined by lattice sums that are never absolutely convergent. The sum depends on the order of summation. The mean zero periodic solution of Poisson's equation, denoted phi, is a natural potential. So is the potential obtained by the Mellin transform algorithm of [Borwein, Borwein, and Taylor, J. Math. Phys., 26 (1985), pp. 2999-3009]. We prove that these two are equal and are both equal to the potential obtained by Abel summation. The sum defining partial derivative(alpha)phi converges absolutely for vertical bar alpha vertical bar >= 3 to partial derivative(alpha)phi. The indeterminacy in the potential is at most a harmonic polynomial of degree 2.
Year
DOI
Venue
2021
10.1137/19M1265697
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Keywords
DocType
Volume
electrostatic potential, Abel summation, Ewald summation, charge group summation, ferro electric
Journal
53
Issue
ISSN
Citations 
2
0036-1410
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Jeffrey Rauch122.54
L. Ridgway Scott2153.63