In this work, we provide a brief review of the mLPDA approach and its application to investigate the Josephson critical currents in ultracold atomic systems, where a potential barrier acts as a weak-link. The strength of this method lies in its ability to treat spatial inhomogeneities and pairing fluctuations on the same footing thus allowing for a reliable description of the entire BCS-BEC crossover at all temperatures in the superfluid phase.
V. et al. (Wed,) studied this question.