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