Boost-invariant perfect Fermi-Dirac spin hydrodynamics

TL;DR

This paper investigates the impact of using Fermi-Dirac statistics instead of Boltzmann approximation in perfect spin hydrodynamics simulations for spin 1/2 particles, showing feasibility and small differences in parameter evolution.

Contribution

It demonstrates the practical implementation of Fermi-Dirac statistics in spin hydrodynamics and compares its effects to Boltzmann approximation, highlighting conditions for numerical stability.

Findings

Differences between Fermi-Dirac and Boltzmann statistics are about one order of magnitude smaller than spin feedback corrections.

Fermi-Dirac integrals can be conveniently parametrized for simulations.

Numerical solutions break down at very large spin polarization values in certain configurations.

Abstract

We analyze the effect of using the Fermi-Dirac statistics, rather than its Boltzmann approximation, in numerical simulations of perfect spin hydrodynamics of particles with spin 1/2. The system considered is boost invariant, transversely homogeneous, with corrections to the baryon current and the energy-momentum tensor that are second order in the spin polarization tensor $\omega$, and the spin tensor considered is first order in $\omega$. The study shows the feasibility of this approach, as the special functions defined by integrals that appear in the coefficients in the Fermi-Dirac case can be conveniently parametrized. For sets of initial conditions used in previous works, the differences in parameter evolution between the two underlying particle statistics are about one order of magnitude smaller than corrections coming from spin feedback. We also discuss when and why the numerical solutions of the equations of perfect spin hydrodynamics break down for very large values of spin polarization in one of the geometric configurations considered.