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Description
Relativistic kinetic theory has been used to describe many aspects of relativistic heavy-ion collisions. To provide smooth initial condition for the hydrodynamic phase from the early stages. To take into account the interaction in the final stage of the evolution, before the chemical and kinetic freeze-out, or directly to replace hydrodynamics in the description of the strongly interacting medium produced in the collision. It has also been used extensively to obtain the transport coefficients of second order hydrodynamics and its generalizations. The relativistic Boltzmann equation is a limiting case for the evolution the Wigner distribution, the quantum precursor of the distribution function. Relativistic kinetic theory is supposed to work for asymptotically weak interactions and small quantum corrections. If the weak interaction assumption is already debatable for a strongly interacting liquid (close to a perfect fluid), more recently it has been shown that the quantum corrections are not small for a free gas[1]. The action scale of the system (compared to the Plank constant) sets the size of these corrections, and a semiclassical expansion is a safe approximation for cold and dilute systems. This is not the case for a hotter and smaller system, like at the beginning of the expansion of the medium. Besides significantly changing the energy density and pressure, hence showing that the quantum corrections are not relevant only for the polarization of spinning particles, the analytic structure of the integrands seem to preclude a semiclassical series to recover the exact results.
These off-shell effects, though, can be taken into account with a generalization of the hydrodynamic expansion [2], recovering second order hydrodynamics (and its transport coefficients), and providing an quantum generalization of the evolution of the non-hydrodynamic modes.
[1] LT, Phys.Rev.D 108 (2023) 7, 076022
[2] LT, Phys.Rev.D 108 (2023) 3, 036015
| Category | Theory |
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