Static response, collective frequencies, and ground-state thermodynamical properties of spin-saturated two-component cold atoms and neutron matter

The thermodynamical ground-state properties and static response in both cold atoms at or close to unitarity and neutron matter are determined using a recently proposed Density Functional Theory (DFT) based on the s-wave scattering length as, effective range re, and unitary gas limit. In cold atoms, when the effective range may be neglected, we show that the pressure, chemical potential, compressibility modulus and sound velocity obtained with the DFT are compatible with experimental observations or exact theoretical estimates. The static response in homogeneous infinite systems is also obtained and a possible influence of the effective range on the response is analyzed. The neutron matter differs from unitary gas due to the non infinite scattering length and to a significant influence of effective range which affects all thermodynamical quantities as well as the static response. In particular, we show for neutron matter that the latter response recently obtained in Auxiliary-Field Diffusion Monte-Carlo (AFDMC) can be qualitatively reproduced when the p-wave contribution is added to the functional. Our study indicates that the close similarity between the exact AFDMC static response and the free gas response might stems from the compensation of the as effect by the effective range and p-wave contributions. We finally consider the dynamical response of both atoms or neutron droplets in anisotropic traps. Assuming the hydrodynamical regime and a polytropic equation of state, a reasonable description of the radial and axial collective frequencies in cold atoms is obtained. Following a similar strategy, we estimate the equivalent collective frequencies of neutron drops in anisotropic traps.