Thermodynamic of a one-dimensional Bose gas at low temperature & superfluidity in neutron-star matter

Ultracold atomic gases and neutron-star matter play a paramount importance in many-body physics, by exhibiting important analogies and differences. One of the most interesting phenomena shared by both systems is provided by superfluidity.

In the first part of the talk, I will show that the chemical potential of a one-dimensional (1D) interacting Bose gas exhibits a non-monotonic temperature dependence which is peculiar of superfluids. The effect is a direct consequence of the phononic nature of the excitation spectrum at large wavelengths exhibited by 1D Bose gases.

For low temperatures T, I demonstrate that the coefficient in the $T^2$ expansion of the chemical potential is defined by the zero-temperature density dependence of the sound velocity and it has been calculated along the crossover between the Bogoliubov weakly-interacting gas and the Tonks-Girardeau gas of impenetrable bosons. The theoretical predictions along the crossover are confirmed by comparison with the exactly solvable Yang-Yang model in which the finite-temperature equation of state is obtained numerically by solving Bethe-ansatz equations.

In the second part of the talk, I will show the results of a study of the superfluid gap in pure neutron matter, associated with the formation of Cooper pairs in the $^1S_0$ channel. The interaction responsible of the onset of superfluidity is an effective interaction coming from a nuclear Hamiltonian strongly constrained by phenomenology and obtained from the correlated basis function (CBF) perturbation theory and the formalism of cluster expansions. The calculations have been carried out using an improved version of the CBF effective interaction, in which three-nucleon forces are taken into account using a microscopic model. Our results show that the superfluid transition occurs at values of densities corresponding to the neutron-star inner crust.