Nanotech 2001 Vol. 2
Nanotech 2001 Vol. 2
Technical Proceedings of the 2001 International Conference on Computational Nanoscience and Nanotechnology

General Theory and Methods Chapter 7

Managing the Distribution of Recursively Calculating Matrix Elements

Authors: L.F. McAven, M. Schlesinger and R.D. Kent

Affilation: University of Windsor, Canada

Pages: 181 - 184

Keywords: distributed processing, group theory, matrix elements, recursion, Racah-Wigner calculus

Abstract:
Interaction stregths and material properties are represented mathematically by matrix elements. The calculation of matrix elements is therefore critical in the interpretation and modelling of physical systems. Part of the matrix elements can be factored out as symmetry coefficeints of the Racah-Wigner Calculus. One powerful, and widely applicable approach to calculating those coefficients, is a recursive technique which expresses higher power coefficients in terms of lower power ones. A recent recursive algorithm is implemented in RACAH, a package for calculating matrix elements of arbitrary Hamiltonians. We discuss issues involving the use of this algorightm in a distributed environment. A major part of distributed efficiency lies in the management of factorisation, simplification and the recursion, and we concentrate on these aspects. Coefficients frequently reappear in recursion and one needs to balance independence against exact non-reproductions.

Managing the Distribution of Recursively Calculating Matrix Elements

ISBN: 0-9708275-3-9
Pages: 218