Resummed spin hydrodynamics from quantum kinetic theory

Abstract

In this work, the equations of dissipative relativistic spin hydrodynamics based on quantum kinetic theory are derived. Employing the inverse-Reynolds dominance (IReD) approach, a resummation scheme based on a power counting in Knudsen and inverse Reynolds numbers is constructed, leading to hydrodynamic equations that are accurate to second order. It is found that the spin dynamics can be characterized by eleven equations: six of them describe the evolution of the components of the spin potential, while the remaining five provide the equation of motion of a dissipative irreducible rank-two tensor. For a simple truncation, the first- and second-order transport coefficients are computed explicitly.

Figures (4)

• Figure 1: The relaxation times for $\omega_0^\mu$, $\kappa_0^\mu$, and $\mathfrak{t}^{\mu\nu}$, as well as the first-order coefficients $\mathfrak{b}$ and $\mathfrak{d}$. The ultra- and nonrelativistic limits are indicated by dashed lines. It can be observed that for large $z$ the relaxation time $\tau_\omega$ increases faster than $\tau_\kappa$ and $\tau_\mathfrak{t}$ by a factor of $z^2$, in agreement with the results of Ref. Wagner:2024fhf.
• Figure 2: The coefficients appearing in the equation for the magnetic part of the spin potential $\omega_0^\mu$ which are not constant in $z$. The ultra- and nonrelativistic limits are indicated by dashed lines.
• Figure 3: The coefficients appearing in the equation for the electric part of the spin potential $\kappa_0^\mu$ which are not constant in $z$. The ultra- and nonrelativistic limits are indicated by dashed lines.
• Figure 4: The coefficients appearing in the equation for the tensor $\mathfrak{t}^{\mu\nu}$ which are not constant in $z$. The ultra- and nonrelativistic limits are indicated by dashed lines.