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Collective excitations in periodic, elastic arrangements of atoms or molecules in condensed matter, like solids and some liquids. They are quasiparticle quantum modes of vibration of elastic structures of interacting particles.
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Are phonons eigenstates of the momentum operator?
:
$$
-i\hbar\nabla \Psi_{n \mathbf{k}}(\mathbf{r})=\hbar \mathbf{k}\Psi_{n \mathbf{k}}(\mathbf{r})+e^{i\mathbf{k}\cdot\mathbf{r}}(-i\hbar\nabla )u_{n\mathbf{k}}(\mathbf{r}) \tag{0}
$$
In the case of Phonons … My question comes from the fact that the demonstration that the electron Bloch function are not eigenstates of the momentum operator Eq. (0) does not hold for phonons, Eq. (2). …
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Why zero chemical potential does not allow the Bose-Einstein Condensation of Phonons?
Transient bose–einstein condensation of phonons. Physics Letters A, 321(5–6):381 – 387, 2004. … So at $T=0$ the number of phonons should be the smallest possible and all should be in the ground state. …