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33


where

t7<


∂ (3π2)5z3(n1∙ + пр5/3


∂n.


10π2


да] -ɪ [<n> + "*>,'3l

U Yl Q-


γ(χ)


∣∆∣2 + Vext. (3.6)


here we ignore the dependence of effective mass on the densities, and define x = njn↑ ∈

[0,1] by assuming the spin ↑ is the majority species. Compared with the mean-field BdG,
we have two extra terms in the diagonal matrix element characterized by Uσ. These two
terms represent the beyond-mean-field self energy experienced by the fermions.

The associated polarization densities nσ-(r), kinetic densities τσ-(r), anomalous densities
v(r), and pairing potential ∆(r) are constructed by summing over all eigenstates Ei weighted
with the Fermi distribution function fβ(E), where β = 1∕T. Here it has been generalized
to the finite temperature case, and as we have mentioned above, in practical calculation,
a small finite temperature can help the initial part of the self-consistent calculations to



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