Suppression of Superfluidity upon Overflow of Trapped Fermions. Quantal and Thomas-Fermi Studies

Two issues will be discussed in this contribution: (i) the generic fact that if a fermionic superfluid in the BCS regime overflows from a narrow container into a much wider one, pairing is much suppressed at the overflow point. Two examples pertinent to the physics of the outer crust of neutron stars and superfluid fermionic atoms in traps will be presented, (ii) A novel Thomas-Fermi approach to inhomogeneous superfluid Fermi-systems is presented and shown that it works well in cases where the local density approximation breaks down.