The name is absent

where

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 U_σ. These two
terms represent the beyond-mean-field self energy experienced by the fermions.

The associated polarization densities n_σ-(r), kinetic densities τ_σ-(r), anomalous densities
v(r), and pairing potential ∆(r) are constructed by summing over all eigenstates E_i 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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