# How a phonon gain momentum?

• atib0539

#### atib0539

Hi guys, I'm reading solid state physics, I have some doubts about phonons.

Here is the question, if we heated up a material, based on the the thermal equilibrium of occupancy of phonons given in Kittel's Introduction to Solid State Physics,

<n> = 1/(e^(\hbar\omega/kBT)-1)

so as T increases, we would excited some extra phonons. But in Introduction to Phonons and Electrons p.124, its states that the phonons would gain some extra momentum when heated up

"Consider a long rod in thermal equilibrium. The net phonon momentum is zero. Now, if we give a push to all the phonons at one end by applying a heat pulse, every phonon gains an extra momentum of equal amount along the direction of the rod. The net momentum is no longer zero but biased with a constant value, which gives rise to a current density of phonons..."

The question is, the excess energy absorbed by the material is to increase the number of phonons without increase the energy of phonons, or to increase the energy of phonons without increase the phonon number? I'm wondering which case is true or they're just using different models, or a combination of both?

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## Answers and Replies

But some articles states that the phonons would gain some extra momentum when the material is heated up when they explaining the thermal conductivity.

Whenever you have something like this, it is the policy of this forum that you cite the source. It is a good practice for when you have to write and publish a paper. Give us the exact citation as if you're writing a paper for publication.

Zz.

Whenever you have something like this, it is the policy of this forum that you cite the source. It is a good practice for when you have to write and publish a paper. Give us the exact citation as if you're writing a paper for publication.

Zz.

Thanks for the advice. :-)