Excitation of identical particles

[SuccessTheory]

Hi. Say you have a cluster of particles and you are probing the cluster with a dopant particle. You excite the dopant and observe its emission - this spectra is perturbed by the cluster particles compared to the free dopant.

What if the dopant was the same as the cluster particles. I know you have to account for a cross term when calculating the spectra in this case because of indistinguishibility, but I'm not sure what's physicallying going on.

Is it either:
1) the energy of the "dopant's" excitation actually spreads across the cluster because they are identical particles, through overlapping wave functions?

2) a statistical effect whereby you are exciting a bunch of particles in the cluster (I'm assuming because there is no "single photon source" to excite only exactly one particle) and can't isolate the emission of the dopant because its the same as the others, and so you end up with some kind of additive effect?

Thanks

 

[LightHero]

!The correct answer is that both of your explanations are correct. The indistinguishability of the particles means that the excited dopant's wavefunction will overlap with the other particles in the cluster, resulting in energy being spread across the particles. Additionally, there will be a statistical effect because the excitation of the dopant will also excite the other particles in the cluster, and you will not be able to differentiate between the emission from the dopant and the emission from the other particles.