3nj Morphogenesis and Semiclassical Disentangling
Abstract
Recoupling coefficients (3nj symbols) are unitary transformations between binary coupled eigenstates of N=(n+1) mutually commuting SU(2) angular momentum operators. They have been used in a variety of applications in spectroscopy, quantum chemistry and nuclear physics and quite recently also in quantum gravity and quantum computing. These coefficients, naturally associated to cubic Yutsis graphs, share a number of intriguing combinatorial, algebraic, and analytical features that make them fashinating objects to be studied on their own. In this paper we develop a bottom--up, systematic procedure for the generation of 3nj from 3(n-1)j diagrams by resorting to diagrammatical and algebraic methods. We provide also a novel approach to the problem of classifying various regimes of semiclassical expansions of 3nj coefficients (asymptotic disentangling of 3nj diagrams) for n > 2 by means of combinatorial, analytical and numerical tools.
Cite
@article{arxiv.1001.4386,
title = {3nj Morphogenesis and Semiclassical Disentangling},
author = {Roger W. Anderson and Vincenzo Aquilanti and Annalisa Marzuoli},
journal= {arXiv preprint arXiv:1001.4386},
year = {2010}
}