Hydrodynamic theories for a system of weakly self-interacting classical ultra-relativistic scalar particles: microscopic derivations and attractors

Abstract

We derive and investigate several hydrodynamic formalisms that emerge from a system of classical, ultra-relativistic scalar particles self-interacting via a quartic potential. The specific form of the total cross-section enables the analytical computation of all transport coefficients that appear in Navier-Stokes (NS), Bemfica-Disconzi-Noronha-Kovtun (BDNK), and second-order transient hydrodynamic theories. We solve all these formalisms in a Bjorken flow scenario and show that NS and BDNK theories display unphysical features when gradients become sufficiently large. This implies that these hydrodynamic approaches may not be suitable to describe the early stages of heavy ion collisions.

30 pages, 8 figures

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• Theories of Relativistic Dissipative Fluid Dynamics
• The regime of applicability of Israel-Stewart hydrodynamics
• Resummed spin hydrodynamics from quantum kinetic theory
• Causal and stable first-order chiral hydrodynamics
• Recent developments in mathematical aspects of relativistic fluids
• Analytical structure of the binary collision integral and the ultrarelativistic limit of transport coefficients of an ideal gas
• Revisiting shear stress tensor evolution: Non-resistive magnetohydrodynamics with momentum-dependent relaxation time
• Modelling stochastic fluctuations in relativistic kinetic theory
• Branch-cut in the shear-stress response function of massless $\lambda {\phi }^4$ with Boltzmann statistics
• Mean free path of photons in relativistic heavy ion collisions
• Convergence of the hydrodynamic gradient expansion in relativistic kinetic theory
• High-order Shakhov-like extension of the relaxation time approximation in relativistic kinetic theory
• Mapping GENERIC hydrodynamics into Carter's multifluid theory
• Hydrodynamic attractor in periodically driven ultracold quantum gases