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These two points of view are not so different in fact. To see that, let's work in the grand-canonical ensemble (which is the most natural to talk about the chemical potential in the Mott phase, since it is not well defined in the canonical ensemble). At a given (and small enough) $t/U$, there is a range of chemical potential $[\mu_-,\mu_+]$ where the ...

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So I think I have managed to figure it out in the end. So we have Bose-Einstein Distribution: $$n_i = \frac{1}{e^{\beta(e_i-\mu)}-1}$$ Now, going off an assumption that the gas is degenerate and that chemical potential is zero, this becomes" $$n_i = \frac{1}{e^{\beta e}-1}$$ Now $\beta = \frac{1}{k_bT}$ I will make another assumption that \$T= T_{crtitical} ...

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After discussion with my colleagues what I understood is If the material is cooled down (to nano kelvin) the wave function of the atom (mainly nuclei) is spread and it got overlapped with neighboring atoms. If the number of atoms within this coherent volume is larger than one (and the atom is a boson i.e. total angular momentum of nuclei and electrons is ...

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Well, in the NJL model you get rid of the gluon. They are considered to be frozen in the low energy limit where you are working because the mass is higher than the energy. Thus you are only working with quarks, and you consider interaction between quarks via effective coupling constants. But in the standard model, gluons (seem to) acquire an effective mass ...

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