Say I have ##n_{a}## bosons in some state ##a##, then the transition rate from some state ##b## to state ##a##, ##W^{boson}_{b\rightarrow a}##, is enhanced by a factor of ##n_{a}+1## compared to the corresponding transition probability for distinguishable particles, ##W_{b\rightarrow a}##, i.e. $$W^{boson}_{b\rightarrow a}=(n_{a}+1)W_{b\rightarrow a}$$ and so the transition rate is from a state ##b## to a state ##a## is enhanced by the number of identical bosonic particles already in the state ##a##.(adsbygoogle = window.adsbygoogle || []).push({});

Conversely, for a fermion, the transition rate is suppressed by a factor of ##1-n_{a}##, i.e. $$W^{fermion}_{b\rightarrow a}=(1-n_{a})W_{b\rightarrow a}$$

My question is, how does one derive these to relations? How does one show that transition rate for bosons are enhanced due to Bose-Einstein statistics, whereas transition rates for fermions are suppressed due to Fermi-Dirac statistics (heuristically I get that in the case of fermions it is due to the Pauli exclusion principle, so called "Pauli blocking")?!

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# I A question on Bose enhancement & Pauli blocking

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