Aspects of neutron superfluidity in the neutron star inner crust

The inner crust of a neutron star is expected to feature a lattice of
neutron rich nuclei in a sea of unbound neutrons. The unbound neutrons
form pairs and are superfluid. I will describe the low energy effective
theory describing the dynamics of this phase of dense matter, applicable
up to temperatures of about a billion Kelvins. Using the theory, we
calculate the heat conductivity due to superfluid phonons, a collective
mode of the superfluid neutron gas, and consider the implications for
crustal heat transport in neutron stars. Due to the large scattering
length between neutrons, the strongly coupled (unitary) Fermi gas is
an interesting model for the neutron superfluid. I will describe a
calculation of the response of the unitary Fermi gas to density
fluctuations, which can be related to the coefficients of the low
energy theory in the absence of the lattice.