David Horgan (quantumtetrahedron): hyperequ1sage26jvscosLv3

This work is based on the paper “Exact Computation and Asymptotic Approximations of 6j Symbols: Illustration of Their Semiclassical Limits by Mirco Ragni et al which I’ll be reviewing in my next post.

The 6j symbols tend asymptotically to Wigner d^l_nm functions when some angular momenta are large where θ assumes certain discrete values.

These formulas are illustrated below:

This can be modelled using sagemath.

The routine gives some great results:

For N=320, M=320, n=0, m=0, l=20, L=0,  Lmax=640

Wigner 6j vs cosθ_L

For N=320, M=320, n=0, m=0, l=10, L=0,  Lmax=640

Wigner 6j vs cosθ_L

For N=320, M=320, n=0, m=0, l=5, L=0,  Lmax=640

Wigner 6j vs cosθ_L