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Fermi distribution 
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#1
Nov1713, 07:47 PM

P: 1,005

All derivations of the Fermidistribution uses a canonical ensemble with a chemical potential, which is the same as to say that the ensemble can exchange particles with a resevoir. But are the derivations still valid for the canonical ensemble with a fixed number of particles and why isn't this just used?



#2
Nov1813, 01:45 AM

Sci Advisor
P: 3,593

The calculation of the grandcanonical partition function is much easier than calculation of the canonical one.
There is a folk theorem that all ensembles are equal in the large N limit, although there are counterexamples. However, I strongly doubt that "All" derivations of the Fermi distribution use a grandcanonical ensemble. E.g. I think Thirrings book "Quantum Mathematical Physics: Atoms, Molecules and Large Systems" contains a derivation using the canonical ensemble. 


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