How can a phonon be localized? A meaningless concept? Yet Kittel...

zhanhai

We shall first determine the origin of phonon.

Lattice waves exist in crystal as lattice modes, and each mode corresponds to phonons of the same frequency and wavevector. My interpretation is that phonon is NOT the lattice mode itself. Rather, phonon is the quanta of interaction between its lattice mode and another object (electron, neutron, ......)

A non-quantized version of equations describing the energy and wavevector relations in lattice mode-electron (neutron....) interaction, partly corresponding to those in Appendix J of Kittel (8th Edition), could be taken as the origin of phonons. Indeed, the energy and wavevector relations of phonon can be derived WITHOUT application of second quantization.

Moreover, I would like to say that second quantization is "source of evils"; it is often introduced prematurely, as it is in some description of eletron-phonon interaction, which should be electron-lattice wave interaction actually.

This issue is far-reaching.

BTW, the same arguments would apply to interaction of light with other objects. What takes part in the interaction, photon or EM wave?

sam_bell

Zhanhai, second quantization is just notation. It makes life simpler; .. or perhaps confusing to those who aren't comfortable with it. And talking about phonons is just a descriptor. But it's a very useful one that gives us a good mental picture that unites it with electrons, photons, etc. and confirms our understanding of wave-particle duality. You don't have to ascribe any deep physical significance to them if you don't want to. Mind you, there are a few people who might wonder if EM fields are _really there_ because we only perceive them through their interactions with charged particles. It doesn't matter. We like to talk about them.

chrisbaird

While I agree with what you are saying, we should be careful not to draw too close the similarities of photons and phonons. Photons are real particles that can exist by themselves as single entities in a vacuum, whereas phonons are not.

sam_bell

Agreed :-) .. On the other hand: Photons are derived as propagating excitations of an underlying EM field, similar to phonons. Note that phonons lose their coherence at high energies in a lattice with anharmonic oscillations. It gives me pause that (I'm told) that QED, QCD, etc. are also expected to breakdown at especially high energies (higher, I assume, than particle colliders can achieve).