Is the number of phonons in crystals conserved?

Phonons in crystals are quantum states associated with vibrations in crystals, and the conservation of the number of phonons in crystals means that the generation and annihilation of phonons are balanced in crystals. In crystals, the number of phonons can be changed by phonon scattering and absorption, which is mainly determined by phonon-phonon interaction and phonon-other particle interaction. Therefore, whether the number of phonons in the crystal is conserved depends on the specific form and intensity of phonon-phonon interaction and phonon-other particle interaction in the crystal.

In phonon-phonon interaction, the interaction between phonons will lead to phonon scattering and absorption. For example, there is inelastic scattering of phonons in crystals, in which one phonon can be scattered to different energy and momentum states. This inelastic scattering process can lead to the change of phonon number, so the phonon number is not conserved under phonon-phonon interaction.

In the interaction between phonons and other particles, the interaction between phonons and other particles will also lead to the scattering and absorption of phonons. For example, there is interaction between phonons and electrons in crystals, and phonons can be absorbed and converted into excited states of electrons. This phonon-electron interaction can lead to the change of phonon number, so the phonon number is not conserved under the phonon-other particle interaction.

In a word, the conservation of phonon number in crystals depends on the specific form and intensity of phonon-phonon interaction and phonon-other particle interaction. In practice, the change of phonon number is usually caused by these interactions, so the phonon number in the crystal is not necessarily conserved.