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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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Why zero chemical potential does not allow the Bose-Einstein Condensation of Phonons?
Bose-Einstein condensation of photons and phonons
However, there are systems where the chemical potential is intrinsically zero even at high temperatures and low densities. … The former is related to the interaction with photonic modes, while the latter is related to the interaction with other particles such as phonons or defects. …