Late-time asymptotic solutions, attractor, and focusing behavior of spin hydrodynamics

TL;DR

This paper studies the late-time behavior and attractor solutions of spin hydrodynamics in Bjorken expansion, revealing focusing phenomena and conditions for spin density decay, thus advancing understanding of spin dynamics in relativistic fluids.

Contribution

It derives asymptotic solutions and identifies attractors and focusing behavior in minimal causal spin hydrodynamics, a novel aspect not observed in traditional hydrodynamics.

Findings

Spin density exhibits power-law decay under specific conditions.

Focusing behavior in spin hydrodynamics is identified.

Spin density can be treated as a hydrodynamic variable at late times.

Abstract

We have investigated the late-time asymptotic solutions, attractor, and focusing behavior of minimal causal spin hydrodynamics in Bjorken expansion. Using the method of dominant balance, we derive the late-time asymptotic solutions of the evolution equation for spin density and identify the specific conditions necessary for the spin density to exhibit a power-law decay. We then analyze both the late-time and early-time attractors for the decay rate of spin density. Additionally, we report the focusing behavior in spin hydrodynamics, which has not been found in conventional relativistic hydrodynamics in Bjorken expansion. Our findings suggest that spin density can be treated as a conventional hydrodynamic variable at late times under certain conditions.