The phonon number is not a conserved quantity, they add up as dictated by the dispersion relation until the Planck distribution is reached. However, I would need the k=PI/a phonons not to disappear from the system.

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    $\begingroup$ Is this for a particular material, or are you looking for a material with this property? Phonons usually decay into other phonons, so I suppose you want to minimise the phonon-phonon coupling of the one you want? The phonons never completely disappear, because of zero-point motion (also, their distribution is Bose-Einstein, not Planck). $\endgroup$ Commented Oct 12, 2022 at 11:07
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    $\begingroup$ In my PhD we worked on a device called saser (by analogy with a laser), where the acoustic phonon emission was controlled by the applied voltage to a double barrier heterostructure. $\endgroup$
    – Camps
    Commented Oct 12, 2022 at 14:10
  • $\begingroup$ Yes, I am looking for a material, which can preserve the phonon-number, the DOS and the Boltzmann distribution together give the Planck distribution. k=PI/a phonons. But the question can also be asked whether the topological protection of k=PI/a phonons can be guaranteed with Weyl points (degenerations) in the Brillouin zone. $\endgroup$ Commented Oct 14, 2022 at 10:10
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    $\begingroup$ user3916292, it's possible that @PhilHasnip and Camps did not see your response to their questions, because you didn't use the @ character to ping them. Since you haven't signed in for 4 months we'll close this as "abandoned" unless you come back or someone says that they'd like to answer the question (just leave a comment)! $\endgroup$ Commented Jun 11, 2023 at 17:02