In boost-invariant cylindrical spin hydrodynamics, azimuthal-longitudinal coupling in the spin tensor produces nonzero total polarization only via the longitudinal magnetic component coupled to the azimuthal electric component.
The ideal relativistic rotating gas as a perfect fluid with spin
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abstract
We show that the ideal relativistic spinning gas at complete thermodynamical equilibrium is a fluid with a non-vanishing spin density tensor \sigma_\mu \nu. After having obtained the expression of the local spin-dependent phase space density f(x,p)_(\sigma \tau) in the Boltzmann approximation, we derive the spin density tensor and show that it is proportional to the acceleration tensor Omega_\mu \nu constructed with the Frenet-Serret tetrad. We recover the proper generalization of the fundamental thermodynamical relation, involving an additional term -(1/2) \Omega_\mu \nu \sigma^\mu \nu. We also show that the spin density tensor has a non-vanishing projection onto the four-velocity field, i.e. t^\mu= sigma_\mu \nu u^\nu \ne 0, in contrast to the common assumption t^\mu = 0, known as Frenkel condition, in the thus-far proposed theories of relativistic fluids with spin. We briefly address the viewpoint of the accelerated observer and inertial spin effects.
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Fermi-Dirac statistics in boost-invariant perfect spin hydrodynamics produce evolution differences about one order of magnitude smaller than spin-feedback corrections, with special functions conveniently parametrized.
The review summarizes developments in spin hydrodynamics, polarization from spin-vorticity coupling, pseudo-gauge freedom, and heavy-flavor spin dynamics in relativistic systems.
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Boost-invariant and cylindrically symmetric perfect spin hydrodynamics
In boost-invariant cylindrical spin hydrodynamics, azimuthal-longitudinal coupling in the spin tensor produces nonzero total polarization only via the longitudinal magnetic component coupled to the azimuthal electric component.
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Boost-invariant perfect Fermi-Dirac spin hydrodynamics
Fermi-Dirac statistics in boost-invariant perfect spin hydrodynamics produce evolution differences about one order of magnitude smaller than spin-feedback corrections, with special functions conveniently parametrized.
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Spin dynamics and polarization in relativistic systems: recent developments
The review summarizes developments in spin hydrodynamics, polarization from spin-vorticity coupling, pseudo-gauge freedom, and heavy-flavor spin dynamics in relativistic systems.