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Hi!
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 shouldn't 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 don't 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 can't 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
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 shouldn't 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 don't 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 can't 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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