Programs in Physics & Physical Chemistry
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|Manuscript Title: Gyutsis: heuristic based calculation of general recoupling coefficients.|
|Authors: D. Van Dyck, V. Fack|
|Program title: GYutsis: VAN DYCK, FACK|
|Catalogue identifier: ADRM_v2_0|
Distribution format: tar.gz
|Journal reference: Comput. Phys. Commun. 154(2003)219|
|Programming language: Java.|
|Computer: Any with Sun's Java 4.1.|
|Operating system: Windows, Linux, Unix.|
|Keywords: Angular momentum, General recoupling coef, Yutsis graph, Reduction rules, Cyclic structure, Heuristic, Computational Methods.|
Nature of problem:
A general recoupling coefficient for an arbitrary number of (integer or half-integer) angular momenta can be expressed as a formula consisting of products of 6-j coefficients summed over a certain number of variables . Such a formula can be generated using the program GYutsis (with a grap hical user front end ) or CycleCostAlgorithm (with a text-mode user fron t end).
Using the graphical techniques of Yutsis, Levinson and Vanagas (1962) a summation formula for a general coupling coefficient is obtained by representing the coefficient as a Yutsis graph and by performing a selection of reduction rules valid for such graphs. Each reduction rule contributes to the final summation formula by a numerical factor or by an additional summation variable. Whereas an optimal summation formula (i.e. with a minimum number of summation variables) is hard to obtain, we present here some new heuristic approaches for selecting an edge from a k-cycle in order to transform it into a (k-1)-cycle (k>3) in such a way that a "good" summation formula is obtained.
From instantaneously for the typical problems to 30 s for the heaviest problems on a Pentium II-350 Linux-system with a 256MB RAM.
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