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Relativistic quantum transport coefficients for second-order viscous hydrodynamics

We express the transport coefficients appearing in the second-order evolution equations for bulk viscous pressure and shear stress tensor using Bose-Einstein, Boltzmann, and Fermi-Dirac statistics for the equilibrium distribution function and Grad's 14-moment approximation as well as the method of Chapman-Enskog expansion for the non-equilibrium part. Specializing to the case of transversally homogeneous and boost-invariant longitudinal expansion of the viscous medium, we compare the results obtained using the above methods with those obtained from the exact solution of the massive 0+1d relativistic Boltzmann equation in the relaxation-time approximation. We show that compared to the 14-moment approximation, the hydrodynamic transport coefficients obtained by employing the Chapman-Enskog method leads to better agreement with the exact solution of the relativistic Boltzmann equation.