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We calculate the parameters of the Ginzburg-Landau (GL) equation of athree-dimensional attractive Fermi gas around the superfluid criticaltemperature. We compare different levels of approximation throughout theBardeen-Cooper-Schrieffer (BCS) to the Bose-Einstein Condensate (BEC) regime.We show that the inclusion of Gaussian fluctuations strongly modifies thevalues of the Ginzburg-Landau parameters approaching the BEC regime of thecrossover. We investigate the reliability of the Ginzburg-Landau theory, withfluctuations, studying the behavior of the coherence length and of the criticalrotational frequencies throughout the BCS-BEC crossover. The effect of theGaussian fluctuations gives qualitative correct trends of the consideredphysical quantities from the BCS regime up to the unitary limit of the BCS-BECcrossover. Approaching the BEC regime, the Ginzburg-Landau equation with theinclusion of Gaussian fluctuations turns out to be unreliable.

Reliability of the Ginzburg-Landau Theory in the BCS-BEC Crossover by Including Gaussian Fluctuations for 3D Attractive Fermions