  In cold atoms and in the crust of neutron stars the pairing gap can reach
values comparable with the Fermi energy. While in nuclei the neutron gap is
smaller, it is still of the order of a few percent of the Fermi energy. The
pairing mechanism in these systems is due to short range attractive
interactions between fermions and the size of the Cooper pair is either
comparable to the inter-particle separation or it can be as big as a nucleus,
which is still relatively small in size. Such a strong pairing gap is the
result of the superposition of a very large number of particle-particle
configurations, which contribute to the formation of the Copper pairs. These
systems have been shown to be the host of a large number of remarkable
phenomena, in which the large magnitude of the pairing gap plays an essential
role: quantum shock waves, quantum turbulence, Anderson-Higgs mode, vortex
rings, domain walls, soliton vortices, vortex pinning in neutron star crust,
unexpected dynamics of fragmented condensates and role of pairing correlations
in collisions on heavy-ions, Larkin-Ovchinnikov phase as an example of a Fermi
supersolid, role pairing correlations control the dynamics of fissioning
nuclei, self-bound superfluid fermion droplets of extremely low densities.
