I have heard that the equivalent to 'stimulated emission' (which occurs with bosons) for fermions is something called 'stimulated inhibition'. Please can someone explain what this processes is, and how it is different from absorption?
(The fact that I can't seem to find any information on it may mean I have the name wrong. If so please can you correct me.)
Beta decay could be considered as something like the weak force equivalent of a spontaneous photon emission in electromagnetism.
If you place the decaying particle in a high density fermi-degenerate environment where the number density of the fermionic decay products (e.g. electrons or positrons) is extremely high, then the decay will be suppressed if the decay fermion cannot be produced with an energy that exceeds the Fermi energy. More directly, it would be impossible for the emitted beta particle to have the same quantum state as an already existing indistinguishable fermion.
I think you could call this "stimulated inhibition".
In the second quantization language, stimulated emission corresponds to the bosonic property $$ a^\dagger|n\rangle=\sqrt{n}|n+1\rangle. $$ That is, the more quanta a mode contains, the higher is the probability of emission into this mode (the relevant coupling term containing operators $a, a^\dagger$ - see this discussion for an example of light coupling to a two-level atom, and this one for coupling in a semiconductor).
On the other hand, for Fermions $$ c^\dagger|n\rangle = \begin{cases} 0, \text{ if } n=1,\\ |1\rangle, \text{ if } n=0\end{cases} $$ That is, if a mode already contains a fermion, another fermion cannot be added to this mode (i.e., its addition is "inhibited") - which is just the Pauli exclusion principle.
