Question: Find the rate of transitions from initial state |i with N p phonons in state p(vector) and N q in state q(vector), and none in

Find the rate of transitions from initial state |i⟩ with N_p phonons in state p(vector) and N_q in state q(vector), and none in any other states, to the final many-body state |f⟩ with N_p − 1 phonons in state p(vector), and N_q − 1 in state q(vector), and one phonon in state p(vector)′, for the interaction term Vint=(Aaaa + Aaaa), a-a-a- kk k k k k,k,k" (4.7.22)

where

This type of term for inelastic phonon scattering will be derived in Section 5.4. Note that the total number of phonons is not conserved.

Vint=(Aaaa + Aaaa), a-a-a- kk k k k k,k,k" (4.7.22)

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