Abstract
Using and comparing kinetic theory and second-order Chapman-Enskog hydrodynamics, we study the non-conformal dynamics of a system undergoing Bjorken expansion. We use the concept of `free-streaming fixed lines' for scaled shear and bulk stresses in non-conformal kinetic theory and hydrodynamics, and show that these `fixed lines' behave as early-time attractors and repellors of the evolution. In the conformal limit, the free-streaming fixed lines reduce to the well-known fixed points of conformal Bjorken dynamics. A new fixed point in the free streaming regime is identified which lies at the intersection of these fixed lines. Contrary to the conformal scenario, both kinetic theory and hydrodynamics predict the absence of attractor behavior in the normalised shear stress channel. In kinetic theory a far-off-equilibrium attractor is found for the normalised effective longitudinal pressure, driven by rapid longitudinal expansion. Second-order viscous hydrodynamics fails to accurately describe this attractor. From a thorough analysis of the free-streaming dynamics in Chapman-Enskog hydrodynamics we conclude that this failure results from an inaccurate approximation of the fixed lines and a related incorrect description of the nature of the fixed point. A modified anisotropic hydrodynamic description is presented that provides excellent agreement with kinetic theory results and reproduces the far-from-equilibrium attractor for the scaled longitudinal pressure.
Highlights
Causal relativistic dissipative hydrodynamics has been surprisingly successful in describing final-state observables in ultrarelativistic collisions among heavy nuclei and between light nuclei [1–10] where the medium is generally expected to be very far from local thermal equilibrium
This has led to a resurgence of interest in understanding the domain of applicability of modern formulations of fluid dynamics [11–34]
It is well known that traditional hydrodynamics, formulated as an order-by-order expansion of the energy-momentum tensor and conserved charges in gradients of temperature, chemical potentials and fluid flow velocity, ceases to be a valid description once the system is far from local equilibrium
Summary
Causal relativistic dissipative hydrodynamics has been surprisingly successful in describing final-state observables in ultrarelativistic collisions among heavy nuclei and between light nuclei [1–10] where the medium is generally expected to be very far from local thermal equilibrium. One way to circumvent this problem is to promote the dissipative fluxes to independent dynamical degrees of freedom of the system whose evolution is governed by relaxation-type equations This approach is taken in the second-order theories of Müller, Israel, and Stewart (MIS) [44–46], where each dissipative quantity relaxes to its Navier-Stokes limit on a microscopic timescale controlled by its corresponding relaxation time. Does second-order nonconformal hydrodynamics [100,101] fail to provide an accurate description of massive kinetic theory in the regime of large Knudsen number, but it is found [98] to be unable to reproduce the attractor that characterizes the underlying microscopic theory [19,102] This seems to contradict the earlier conclusion from conformal studies that hydrodynamics is applicable even far away from equilibrium.
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