Application of novel relaxation time approximation for the Boltzmann equation in relativistic fluid dynamics - Piipponen, Mika (2024)
Ultrarelativistic heavy-ion collisions are modelled with relativistic fluid dynamics. Since quark-gluon plasma formed in collider experiments cannot be directly measured, the investigation of the substance is heavily based on comparing experimental data to predictions of theoretical models. In this thesis we review a novel relaxation time approximation for the relativistic Boltzmann equation, which is fully compatible with the macroscopic conservation laws. We calculate approximations for the temperature dependence of bulk viscosity, particle diffusion coefficient and shear viscosity of a fluid employing this model. The calculation is carried out by matching the fluid dynamical quantities with the underlying microscopic theory, where the single particle momentum distribution function is expressed using first order Chapman–Enskog expansion. In this way, even with energy-dependent relaxation times, we achieve consistent approximations for the fluid dynamical transport coefficients that are in full agreement with the second law of thermodynamics. The novel relaxation time approximation can be utilized to construct effective kinetic descriptions for matter in heavy-ion collisions.