SEMINAR ANNOUNCEMENT: “Thermodynamic behavior of a one-dimensional Bose gas at low temperature and superfluidity in neutron-star matter"

Giulia De Rosi

INO-CNR BEC Center and Dipartimento di Fisica,

Università di Trento, Italy

“Thermodynamic behavior of a one-dimensional Bose gas at low

temperature and superfluidity in neutron-star matter"

Abstract

In the first part of the seminar, 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. Finally, we have estimated finite-size

effects for a 1D ring geometry with periodic boundary conditions at

zero-temperature for various thermodynamic functions, pointing out the

occurrence of important deviations from the thermodynamic limit.

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 $^1S_0$ sector. 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.

References:

[1] G. De Rosi, G. E. Astrakharchik and S. Stringari "Thermodynamic

behavior of a one-dimensional Bose gas at low temperature" Phys. Rev.

A 96, 013613 (2017)

[2] O. Benhar and G. De Rosi "Superfluid Gap in Neutron Matter from a

Microscopic Effective Interaction" arXiv: 1705.06607 (2017)