Nonlinear causality and stability of perfect spin hydrodynamics and its nonperturbative character

TL;DR

The paper addresses the formulation of perfect spin hydrodynamics for spin-1/2 particles and the need to ensure causal, stable evolution in a relativistic setting. It generalizes prior work to include quantum spin and both Boltzmann and Fermi-Dirac statistics by defining a generating function $\chi$ and conserved currents $N^{\lambda A}$ to test the divergence-type theory criteria. The main contributions show nonlinear causality and stability for four combinations via the positivity of $M^{\lambda}$ and its decomposition into positive weights, highlighting a nonperturbative character since exact distribution functions are used. The results imply these formulations are numerically viable for simulating spin dynamics in relativistic fluids, such as the quark–gluon plasma produced in heavy-ion collisions.

Abstract

Four formulations of perfect spin hydrodynamics for spin-1/2 particles, distinguished by their treatment of spin (classical vs. quantum) and by the underlying particle statistics (Boltzmann vs. Fermi-Dirac), are analyzed and shown to satisfy the requirements of a divergence-type theory. Moreover, for all the formulations, we define the generating functions associated with the relevant thermodynamic currents and demonstrate that the constructed hydrodynamic theory is nonlinearly causal and stable. The latter is achieved by employing the exact expressions for the distribution functions, indicating a nonperturbative character of our approach.