thermodynamics - Do gases have phonons?

A phonon is a quantized unit of sound; they are encountered when quantizing lattice vibrations in solids. Now, even an ideal gas supports sound waves, but in this case, interactions between atoms are weak. That makes it hard to imagine what a quantized vibration would look like, since at small scales, the particles are free!

Is there a phonon picture for sound in an ideal gas? Is it ever useful?

Answer

The only mention of this subject I can recall seeing is an aside in Xiao-Gang Wen's book, Quantum Field Theory of Many-Body Systems. Footnote on page 86:

A sound wave in air does not correspond to any discrete quasiparticle. This is because the sound wave is not a fluctuation of any quantum ground state. Thus, it does not correspond to any excitation above the ground state.

I'm not completely sure that I buy this, but it does certainly identify a crucial point. Plasmons or phonons in a condensed matter setting both have a restoring force, which lets one identify a minimum energy state to excite. In your typical view of an ideal gas, in which atoms mostly travel freely but occasionally collide with one another in some short-ranged way, this is not really true. You can make all sorts of density patterns in which the atoms are still not actually touching and thus the energy is not increased.

One might be tempted to get around this by taking a continuum limit somehow and considering a smooth quantum fluid, but then you are by definition trying to quantize a macroscopic field, which does not seem to make sense in even a formal way. In particular, since the field is a coarse-graining of the true system, one has necessarily thrown away some degrees of freedom, which means that the state of the field is never a pure quantum state and is more likely very close to a fully decohered statistical mixture.

In contrast, in a system with long-range interactions, and some boundary conditions, I would assume that phonon-like excitations are possible because the restoring force from mutual repulsion provides a well-defined ground state. This is a Coulomb crystal (1). But clearly this is very far from an ideal gas.

Edit: I should emphasize, as @Xcheckr has, that the above answer is interpreting the OP's question to refer to a Maxwell-Boltzmann ideal gas in a high-temperature state. There is of course no obstacle to defining the ground state of a BEC of an alkali gas, and such a ground state does indeed have phonon excitations (assuming a weak interaction). Similar remarks apply to a degenerate Fermi gas.