Perturbative approaches in relativistic kinetic theory and the emergence of first-order hydrodynamics

Abstract

Hydrodynamics can be formulated in terms of a perturbative series in derivatives of the temperature, chemical potential, and flow velocity around an equilibrium state. Different formulations for this series have been proposed over the years, which consequently led to the development of various hydrodynamic theories. In this work, we discuss the relativistic generalizations of the perturbative expansions put forward by Chapman and Enskog, and Hilbert, using general matching conditions in kinetic theory. This allows us to describe, in a comprehensive way, how different out-of-equilibrium definitions for the hydrodynamic fields affect the development of the hydrodynamic perturbative series. We provide a perturbative method for systematically deriving the hydrodynamic formulation recently proposed by Bemfica, Disconzi, Noronha, and Kovtun (BDNK) from relativistic kinetic theory. The various transport coefficients that appear in BDNK (at first-order) are explicitly computed using a new formulation of the relaxation time approximation for the Boltzmann equation. Assuming Bjorken flow, we also determine the hydrodynamic attractors of BDNK theory and compare the overall hydrodynamic evolution obtained using this formulation with that generated by the Israel-Stewart equations of motion and also kinetic theory.

Far-from-equilibrium kinetic dynamics of $λϕ^4$ theory in an expanding universe

“…One may also check if the generating function method introduced here is useful when investigating the dynamics of systems of more relevance to heavy-ion collisions, such as QCD effective kinetic theory [30][31][32][33][34][35] and models where the particles in the gas have a temperature-dependent mass [36][37][38][39][40][41][42]. Furthermore, a better understanding of how the vector and tensor parts of the spectrum behave in our system would be relevant when studying the emergence of hydrodynamic attractors [43][44][45] and the characterization of the far-fromequilibrium properties of kinetic theory systems [21,22,25,[46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63]. We hope to report on our progress in some of the topics mentioned above in the near future.…”