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I was looking at the high- and low-temperature limits of the specific heat in the quantum theory of cristals (Ashcrof&Mermin, Chap. 23).

To get the behavior under these limits, one consider first the case where T is large compared with all the phonon frequencies and second, when T is low compared to these frequencies.

But, the temperature shouldnt be (in some way) proportionnal to the phonon frequency? If this was right, then the low limit [tex]\omega\gg T[/tex] would be a non-sense.

So I realize that I dont really understand the relation between temperature and phonons. Sure, I know that the number of phonon of each type will come to play, but I cant make a whole picture of all that in my head.

Can someone try to explain, or give some refs where this is clearly explained?

Thanks a lot,

TP

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# Temperature vs phonon

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