Numerical work with sagemath 23: Wigner Reduced Rotation Matrix Elements as Limits of 6j Symbols

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 dlnm functions when some angular momenta are large where θ assumes certain discrete values.

hyperequ10

 

hyperequ11

 

hyperequ12

 

These formulas are illustrated below:

hyperfig2

 

 

This can be modelled using sagemath.

hyperequ1sage1

The routine gives some great results:

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

Wigner 6j vs cosθL

hyperequ1sage26jvscosL

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

Wigner 6j vs cosθL

hyperequ1sage26jvscosLv2

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

Wigner 6j vs cosθL

hyperequ1sage26jvscosLv3

 

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