3nj Morphogenesis and Semiclassical Disentangling

TL;DR

This paper introduces a systematic method for generating 3nj recoupling coefficients and classifying their semiclassical expansion regimes using combinatorial, algebraic, and numerical techniques.

Contribution

It develops a bottom-up approach for constructing 3nj coefficients from lower-order diagrams and offers a new classification method for their semiclassical asymptotic behavior.

Findings

New systematic procedure for generating 3nj from 3(n-1)j diagrams.

Novel classification approach for semiclassical regimes of 3nj coefficients.

Application of combinatorial, analytical, and numerical tools to study asymptotic 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.