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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

<n> = 1/(e^(\hbar\omega/k

so as T increases, we would excited some extra phonons. But in

"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?

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/k

_{B}T)-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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