The name is absent

27

partially polarized intermediate region becomes comparable to or even larger than that of
the BCS core. Accompanied with the oscillation in order parameter, the density profiles
also exhibit strong oscillations with the minority component possessing a larger oscillation
amplitude than the majority component.

We are trying to check the existense Chandraskhar-Clogston limit in our calculation,
which is also a major difference between experiments at MIT and Rice. For high polar-
ization, the canonical BdG Calaculation is very hard to converge to a steady state, we were
only able to perform a calculation up to P = 0.7 for λ = 50. We are trying to use the
ground-canonical Calcualtion to investigate how system behaves above this polarization.

3.3.2 Larger particle number at T - 0.02Tf

Beyond the systematic investigation for 200 particles at zero temperature, we have suc-
cessfully obtained some converged results for different particle number ranging from 200
around 2000 by setting temperature T = 0.027^,∕.∙. With these data, we can study the fi-
nite size effect by looking at the density profiles at the approximately same polarization
corresponding to different particle numbers. In Fig. 3.6, we compare a series of density
profiles at T = 0.0277 with different particle number A = 206,440,1083 at P ≈ 0.38. We
observed that the majority and minority densities along radial direction still overlap when
particle number goes up to N = 440 while such overlap disappears when the particle num-
ber is increased to N - 1083. Therefore it seems that this LDA breakdown phenomenon
we observed for 200 particles can be considered as a finite-size effect. The further inves-

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