When can we treat identical particles as distinguishable? An unfamiliar classical limit

Details When can we treat identical particles as distinguishable? An unfamiliar classical limit When can we treat identical particles as distinguishable? An unfamiliar classical limit

Feb 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985amjph..53..119i&link_type=abstract

American Journal of Physics, Volume 53, Issue 2, pp. 119-122 (1985).

Physics

2

Fermion Systems And Electron Gas

Scientific paper

Consider a system of N identical particles having an internal degree of freedom α whose energy enters additively. In statistical mechanics the question arises, ``When can we compute the equilibrium properties related to α as if the system were a collection of N noninteracting distinguishable particles?'' Most texts leave the student very unclear about this. Consider the case α=intrinsic spin. Then for a paramagnetic solid the answer is ``for any density, temperature, or B field.'' For an ideal gas we find the general answer ``if and only if <<1, all single particle states r, that is, degeneracy effects are negligible.'' It is well known that this criterion is necessary for the so-called ``classical limit'' of low densities or high temperatures. However, it is not equivalent to it; this generalized classical regime can hold for arbitrary densities or temperatures, and lead to unfamiliar magnetic properties, if the B field is strong enough. In other words, very strong B fields can inhibit degeneracy even for high densities or low temperatures. Neutron stars are briefly considered.

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