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The $\pi$-meson is a boson, but consists of quark-antiquark (fermions). It seems to me that at some energy level (equivalently distance) the inner structure (fermionic nature of the quarks) of the particle in question should become important and the bosonic nature less so.

Question:
Can we have a bunch of pions occupying the same quantum state at all temperatures, or is this model bound to fail due to the fermionic nature of its constituents?

I'm thinking for example of the pion-cloud (in some models) surrounding the nuclei.

EDIT: I found this question which is very related to the present one. Although I should add that my question (regarding the pion-cloud) is more specific and less general.

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I think the answer is it depends on distance (relative to the size of your system). Another well known example of a boson which is comprised of fermionic components is the helium-4 atom, which has integer spin (both the nucleus and the neutral atom itself).

Fermionic or bosonic behavior of a composite particle (or system) is only seen at large (compared to size of the system) distance. At proximity, where spatial structure begins to be important, a composite particle (or system) behaves according to its constituent makeup. For example, two atoms of helium-4 cannot share the same space if it is comparable in size to that of the inner structure of the helium atom itself (~10−10 m)—despite bosonic properties of the helium-4 atoms. Thus, liquid helium has finite density comparable to the density of ordinary liquid matter.

(Taken from here.) I think this provides a concrete example of what you were asking. Hopefully this helps.

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Cool. That is what my intuition said. –  Love Learning Dec 16 '13 at 18:10
    
Or I might have read it somewhere a long time ago? I don't know. –  Love Learning Dec 16 '13 at 18:24

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