Fate of spin polarization in a relativistic fluid: An entropy-current analysis

Abstract

We derive relativistic hydrodynamic equations with a dynamical spin degree of freedom on the basis of an entropy-current analysis. The first and second laws of local thermodynamics constrain possible structures of the constitutive relations including a spin current and the antisymmetric part of the (canonical) energy-momentum tensor. Solving the obtained hydrodynamic equations within the linear-mode analysis, we find spin-diffusion modes, indicating that spin density is damped out after a characteristic time scale controlled by transport coefficients introduced in the antisymmetric part of the energy-momentum tensor in the entropy-current analysis. This is a consequence of mutual convertibility between spin and orbital angular momentum.

Local spin polarization in high energy heavy ion collisions

“…This suggests that if the spin is (quasi-)conserved, after polarized in the early stage by the OAM, the pressure gradient would be possibly drive a similar φ p dependence as that for the T-vorticity. This may be verified by the simulation using spin hydrodynamics [73,75].…”

“…In relativistic hydrodynamics, in order to obtain the spin vector, we need to first obtain T , u µ , and Ω µν by solving the hydrodynamic equations in which the spin degree of freedom (or equivalently Ω µν ) is treated on the same footing as T and u µ . Such a framework is the spin hydrodynamics [73,75]. However, the numerical spin hydrodynamics has not been established yet.…”

“…(8) and (13) that ω (T ) µν (T ) and ω (th) µν (T ) have the opposite sign. The importance of the thermal vorticity relies on the fact that at global equilibrium, Ω µν equals to ω (th) µν provided that the energy-momentum tensorT µν has a nonvanishing anti-symmetric component [72,75,85]. This can be seen from the following procedure (the analysis based on the dissipative spin hydrodynamics or the kinetic theory gives the same conclusion).…”

“…This calls for new approaches, for examples, the spin can be treated as an independent dynamical variable in the spin kinetic theory and spin hydrodynamics, or dissipative terms should be considered which are possibly larger than believed. Recently, the framework of spin hydrodynamics was developed [73][74][75]. The spin evolution based on particle collisions was derived [76].…”

“…The purpose of the present paper is not to make a numerical study based on these new approaches, instead, our purpose is much less ambitious: we will explore different choices of the so-called "spin chemical potential" Ω µν and calculate the corresponding local hyperon polarization. The underlying reason is that, beyond global equilibrium, the thermal vorticity is not guaranteed to be the spin chemical potential, and thus the latter becomes a free parameter [72,74,75]. In the (3+1)D hydrodynamic model CLVisc [77,78], we will assume that the spin chemical potential Ω µν is still determined by the fluid velocity and temperature (or equivalently the energy density).…”