Boundary conditions for star matter and other periodic fermionic systems

TL;DR

This paper compares two methods for handling boundary conditions in simulations of bulk fermionic matter, highlighting their differences in variational approaches and demonstrating applications with Fermionic Molecular Dynamics.

Contribution

It establishes the formal relation between Twist Averaged Boundary Conditions and Wannier-based approaches, clarifying their differences in variational methods for stellar matter.

Findings

The two methods coincide for exact eigenstates.

Differences arise in variational approaches.

Model applications with Fermionic Molecular Dynamics are demonstrated.

Abstract

Bulk fermionic matter, as it can be notably found in supernova matter and neutrons stars, is subject to correlations of infinite range due to the antisymmetrisation of the N-body wave function, which cannot be explicitly accounted for in a practical simulation. This problem is usually addressed in condensed matter physics by means of the so-called Twist Averaged Boundary Condition method. A different ansatz based on the localized Wannier representation has been proposed in the context of antisymmetrized molecular dynamics. In this paper we work out the formal relation between the two approaches. We show that, while the two coincide when working with exact eigenstates of the N-body Hamiltonian, differences appear in the case of variational approaches, which are currently used for the description of stellar matter. Some model applications with Fermionic Molecular Dynamics are shown.