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Kohn Anomaly and Avoided Crossing (Anticrossing/Level Repulsion) are terms that are found to be used when discussing phonon dispersion. The former (see last paragraph, page 198) is related to electron-phonon coupling, while the latter (refer 2nd paragraph, page 55) is related to phonon-phonon coupling. Both phenomena lower the phonon frequency.
$\begingroup$I gave my +1 long ago, but I wonder if there's any update you can give us after all these months? Also, are you still actively in need of an answer to this question?$\endgroup$
$\begingroup$Thanks for the response AbPhys! If anyone has an answer, they're encouraged to ping me in a comment here, or to write a Flag asking for the question to be re-opened!$\endgroup$
