Ideal spin hydrodynamics from Wigner function approach

TL;DR

This paper derives ideal spin hydrodynamics equations from the Wigner function approach, incorporating spin polarization effects and extending traditional hydrodynamics with quantum statistical considerations.

Contribution

It introduces a Wigner function-based framework to derive hydrodynamical quantities for polarized spin-1/2 particles, including new spin-related terms at first and second order in Knudsen number.

Findings

Derived hydrodynamical quantities with spin polarization

Extended ideal hydrodynamics to include spin effects

Formulated equations of motion for thermodynamical parameters

Abstract

Based on the Wigner function in local equilibrium, we derive hydrodynamical quantities for a system of polarized spin-1/2 particles: the particle number current density, the energy-momentum tensor, the spin tensor, and the dipole moment tensor. Comparing with ideal hydrodynamics without spin, additional terms at first and second order in the Knudsen number $\text{Kn}$ and the average spin polarization $\chi_s$ have been derived. The Wigner function can be expressed in terms of matrix-valued distributions, whose equilibrium forms are characterized by thermodynamical parameters in quantum statistics. The equations of motions for these parameters are derived by conservation laws at the leading and next-to-leading order $\text{Kn}$ and $\chi_s$.