How to distinguish different phonon branches?

[qiub]

Hi, I'm trying to distinguish phonon branches in the case of branch crossings in some complex phonon dispersions, like in the below example:

http://cmt.dur.ac.uk/sjc/thesis/thesis/img354.gif

My question is, how can I know which portions near the crossing belong to the same branch? I've this question because when I want to calculate group velocity, it becomes quite confusing, please help me, thanks!

[genneth]

Quite often, there are distinguishing features between the branches near a crossing point, so it is not really possible to say which line belongs to which. One general method is to postulate a phonon-phonon interaction (say, universal repulsion), which will cause the crossing points to be teased apart, and thus reveal some underlying differences (maybe, depends on the interaction).

[qiub]

Thanks for the reply! I also got another reply from other sources. He suggested that the way to determine which frequencies belong to the same branch, a dot product of eigenvectors from neighboring k points can be carried out, the ones with most overlap should be belong to the same branch.