Time-Dependent Superfluid Band Theory for the Inner Crust of Neutron Stars: Current Status and Future Challenges

TL;DR

This paper reviews the development of a time-dependent superfluid band theory for neutron star crusts, highlighting its potential to improve understanding of neutron transport properties in superfluid nuclear matter.

Contribution

It introduces a novel fully-microscopic, time-dependent band theory based on TDDFT that accounts for superfluidity, advancing the study of neutron behavior in neutron star crusts.

Findings

Successful development of a parallel computational code

Application to the slab phase of nuclear matter

Discussion of future research directions

Abstract

In this contribution, current status and future prospects of our ongoing project is summarized. In the inner crust of neutron stars, a variety of crystalline structures may emerge, as a result of competition of Coulomb and nuclear interactions, which are immersed in a sea of superfluid neutrons. The best quantum mechanical approach to study properties of dripped neutrons under a periodic potential is the band theory of solids. Concerning the band structure effects on transport properties of neutrons, however, situation is complicated and there has not been established a clear consensus yet. To provide a robust conclusion on the band structure effects, we have developed a fully-microscopic time-dependent band theory based on time-dependent density functional theory (TDDFT), taking full account of Fermionic superfluditiy. We have successfully developed a parallel computational code and applied it to the slab phase of nuclear matter. We introduce ongoing works and discuss possible future directions.