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Phonons are the quanta of vibrations in a crystal lattice. As the name suggest, phonons are already a quantum phenomena but when studying heat transfer the phonons are mostly very classical (wave mechanics, semiclassical treatment).

Usually the quantum characteristics enter into the statistics (bosons statistics) but not much else. Do phonons display any evidently quantum phenomenona?

Can there be entangled phonons? When could quantum effects for phonons become important in transport?

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  • $\begingroup$ Yes there can be entangled phonons but I am no expert. Here is a paper that discusses entangled phonons. pme.uchicago.edu/news/…. $\endgroup$ May 20, 2022 at 23:09

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One example is a phonon-polariton, which is a coherent quasiparticle made from light and optical phonons.

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  • $\begingroup$ Could you be more specific on which kind of quantum properties does that exhibit? $\endgroup$
    – Mauricio
    May 21, 2022 at 11:03

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