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I'm learning about phonons and I read that for a phononic gas to reach equilibrium the phonon waves need to lose momentum when they collide. However in an ideal gas the momentum is always preseved. Could anyone comment on this interesting requirement for phoninic gases?

bodacydo
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I'm not sure that I agree with that statement. What's your source?

At equilibrium, a phonon gas will have zero momentum. However, the converse it not true: you can have a phonon gas out of equilibrium but with zero momentum. In that case, it can approach equilibrium without losing any momentum, since it has none to begin with!

Although we have both used the term "momentum", remember that phonons are not real particles; they're quasiparticles. So, they do not have real momentum; they have quasimomentum. The real momentum of a phonon mode is zero (with one minor exception). This is because, in each mode, there a just as many atoms moving one direction as the other, so they cancel out. Moreover, quasimomentum does not have to be conserved; it only has to be conserved up to a reciprocal lattice vector. (If you want a derivation see a text on the subject, like Ziman or Ashcroft and Mermin.)

lnmaurer
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