Analytic solutions of relativistic dissipative spin hydrodynamics with Bjorken expansion

Abstract

We have studied analytically the longitudinally boost-invariant motion of a relativistic dissipative fluid with spin. We have derived the analytic solutions of spin density and spin chemical potential as a function of proper time $\tau$ in the presence of viscous tensor and the second order relaxation time corrections for spin. Interestingly, analogous to the ordinary particle number density and chemical potential, we find that the spin density and spin chemical potential decay as $\sim {\tau }^{-1}$ and $\sim {\tau }^{-1/3}$, respectively. It implies that the initial spin density may not survive at the freezeout hyper-surface. These solutions can serve both to gain insight on the dynamics of spin polarization in relativistic heavy-ion collisions and as testbeds for further numerical codes.

14 pages

References in corpus (17)

• Angular momentum conservation in heavy ion collisions at very high energy
• Lorentz Invariance in Chiral Kinetic Theory
• Collective longitudinal polarization in relativistic heavy-ion collisions at very high energy
• Fate of spin polarization in a relativistic fluid: An entropy-current analysis
• Collisions in Chiral Kinetic Theory
• Global $\Lambda$ Polarization in high energy collisions
• Lambda hyperon polarization in relativistic heavy ion collisions from the chiral kinetic approach
• Stability and Causality in relativistic dissipative hydrodynamics
• Relativistic spin hydrodynamics with torsion and linear response theory for spin relaxation
• Chiral transport equation from the quantum Dirac Hamiltonian and the on-shell effective field theory
• The ideal relativistic spinning gas: polarization and spectra
• Reexamination of local spin polarization beyond global equilibrium in relativistic heavy ion collisions
• A hydrodynamic study of hyperon spin polarization in relativistic heavy ion collisions
• Spin polarization evolution in a boost invariant hydrodynamical background
• Anomalous magnetohydrodynamics with longitudinal boost invariance and chiral magnetic effect
• Pseudoscalar condensation induced by chiral anomaly and vorticity for massive fermions
• Shear viscosity coefficient and relaxation time of causal dissipative hydrodynamics in QCD

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