Coulomb potentials in two and three dimensions under periodic boundary conditions

A method to sum over logarithmic potential in 2D and Coulomb potential in 3D with periodic boundary conditions in all directions is given. We consider the most general form of unit cells, the rhombic cell in 2D and the triclinic cell in 3D. For the 3D case, this paper presents a generalization of Sperb's work [R. Sperb, Mol. Simulation, \textbf{22}, 199-212(1999)]. The expressions derived in this work converge extremely fast in all region of the simulation cell. We also obtain results for slab geometry. Furthermore, self-energies for both 2D as well as 3D cases are derived. Our general formulas can be employed to obtain Madelung constants for periodic structures.Comment: Generalization of the work done in cond-mat/0405574. To appear in J. Chem. Physics. A few typos have been correcte

Implications of Globalization for the Output-inflation Relationship: An Assessment

During the past two decades, a growing body of research has explored the implications of increased trade and financial openness for the relationship between output and inflation. This paper reviews proposed theoretical channels through which the degree of openness might ultimately affect the output-inflation trade-off and surveys the empirical studies that have sought to determine the net effect of greater openness on this trade-off. In addition, the paper utilizes a single cross-country data set to evaluate, taking into account recent developments in the literature, the likely sign and significance of this net effect. In particular, we find current data imply that there is a negative and significant relationship between openness and the sacrifice ratio, regardless of the transmission channel that is proposed

Effective way to sum over long range Coulomb potentials in two and three dimensions

I propose a method to calculate logarithmic interaction in two dimensions and coulomb interaction in three dimensions under periodic boundary conditions. This paper considers the case of a rectangular cell in two dimensions and an orthorhombic cell in three dimensions. Unlike the Ewald method, there is no parameter to be optimized, nor does it involve error functions, thus leading to the accuracy obtained. This method is similar in approach to that of Sperb [R. Sperb, Mol. Simulation, 22, 199 (1999).], but the derivation is considerably simpler and physically appealing. An important aspect of the proposed method is the faster convergence of the Green function for a particular case as compared to Sperb's work. The convergence of the sums for the most part of unit cell is exponential, and hence requires the calculation of only a few dozen terms. In a very simple way, we also obtain expressions for interaction for systems with slab geometries. Expressions for the Madelung constant of CsCl and NaCl are also obtained.Comment: To appear in Phy. Rev.