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Weak coupling to unitarity crossover in Bose-Fermi mixtures: Mixing-demixing transition and spontaneous symmetry breaking in trapped systems

Weak coupling to unitarity crossover in Bose-Fermi mixtures: Mixing-demixing transition and spontaneous symmetry breaking in trapped systems

The usual treatment of a Bose-Fermi mixture relies on weak-coupling Gross-Pitaevskii (GP) and density-functional (DF) Lagrangians, often including the more realistic perturbative Lee-Huang-Yang (LHY) corrections. We suggest analytic non-perturbative beyond-mean-field Bose and Fermi Lagrangians valid along the crossover from weak- to strong-coupling limits of intraspecies interactions consistent with the LHY …