Abstract
Universality and crossover is described for attractive and repulsive interactions where, respectively, the BCS-BEC crossover takes place and a ferromagnetic phase transition is claimed. Crossovers are also described for optical lattices and multicomponent systems. The crossovers, universal parameters and phase transitions are described within the Leggett and NSR models and calculated in detail within the Jastrow-Slater approximation. The physics of ultracold Fermi atoms is applied to neutron, nuclear and quark matter, nuclei and electrons in solids whenever possible. Specifically, the differences between optical lattices and cuprates is discussed w.r.t. antiferromagnetic, d-wave superfluid phases and phase separation.
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