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phonon DOS vs ELIASBERG FUNCTION http://epwforum.uk/viewtopic.php?f=7&t=431 
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Author:  topgun [ Fri Dec 29, 2017 8:14 pm ] 
Post subject:  phonon DOS vs ELIASBERG FUNCTION 
dear all, what is the difference between phonon DOS and eliasberg spectral function? how the latter is different from the former? if we have DOS what is the need for eliasberg spectral function? regards top gun 
Author:  adenchfi [ Fri May 31, 2019 1:55 pm ] 
Post subject:  Re: phonon DOS vs ELIASBERG FUNCTION 
If by the Eliashberg function, you mean alpha^2 f(omega), then the difference is easy. Phonon DOS = F(omega) Eliashberg spectral function = alpha^2 (omega) F(omega), where alpha^2 is the electronphonon coupling. One can think of the eliashberg spectral function as an electronmodified phonon DOS, I guess. I recommend you read the EPW paper(s) for more answers. I know this answer is late, but perhaps others will benefit from the quick answer. 
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