May 16, 2009
I’ve settled for a “sketchy” understanding of the vast amount of literature that relates to my project. This has let me try to remember the take-home messages of a hundred papers or so, piece them together and attain a certain level of “proper” conversation with my supervisor. But it’s not helping with the literature review part of my report, which demands quite a lot more precision.
May 8, 2009
Mostly for my benefit, I’m looking for a simple way to compare the canonical and grand canonical ensembles in statistical physics. How about this…
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The canonical ensemble is a load of “systems”, each of which has a set of energy levels, and can exchange energy with all the other systems.
The probability of a system being in the ith state, whose energy is E_i, is:
where Z is the system’s partition function.
The systems don’t have to be identical, but different systems have different Z’s.
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The grand canonical ensemble is a load of “systems”, each of which has a set of “legal” particle numbers: , … (probably 0, 1, 2…) and has a set of energy levels for each particle number, and can exchange energy and particles with all the other systems.
The probability of a system being in state (r,s), meaning it has particles and total energy , is:
where X is the system’s grand partition function. is called chemical potential. Now to explain that…