In a rigidly rotating free Fermi gas, the relativistic Barnett effect produces different Fermi energies for spin-up and spin-down fermions, leading to a moment of inertia that scales as 1/T at high temperature, analogous to the Curie law.
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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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Relativistic Barnett effect and Curie law in a rigidly rotating free Fermi gas
In a rigidly rotating free Fermi gas, the relativistic Barnett effect produces different Fermi energies for spin-up and spin-down fermions, leading to a moment of inertia that scales as 1/T at high temperature, analogous to the Curie law.
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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.