Viscosity, wave damping, and shock-wave formation in cold hadronic matter

Abstract

We study linear and nonlinear wave propagation in a dense and cold hadron gas and also in a cold quark-gluon plasma, taking viscosity into account and using the Navier-Stokes equation. The equation of state of the hadronic phase is derived from the nonlinear Walecka model in the mean-field approximation. The quark-gluon plasma phase is described by the MIT equation of state. We show that in a hadron gas viscosity strongly damps wave propagation and also hinders shock-wave formation. This marked difference between the two phases may have phenomenological consequences and lead to new quark-gluon plasma signatures.

Nonlinear waves in second order conformal hydrodynamics

“…In the limit τ 0 π → 0 one recovers the linear wave equation for the viscous fluid described by the relativistic Navier-Stokes theory [21,34]. Also, setting τ 0 π = χ = 0, one obtains the linear wave equation for the ideal relativistic fluid [21,34].…”

“…In order to obtain the simplest wave equation for a small perturbation in the fluid around equilibrium, one can resort to the formalism known as the "linearization formalism" [20,21,34], in which one performs the following expansions of the energy density, pressure, shear stress tensor, and fluid 4-velocity around their respective equilibrium configuration values (for simplicity, here we take the sound wave disturbances in the "x" direction)…”

“…Also, setting τ 0 π = χ = 0, one obtains the linear wave equation for the ideal relativistic fluid [21,34].…”

“…Setting only τ π 0 → 0, (13) gives the Navier-Stokes sound wave dispersion relation [21] (13) is rewritten as a dimensionless equation to be solved forω…”

“…The propagation of perturbations through a QGP has been investigated in several works with the help of a linearized version of the hydrodynamics of perfect fluids and of viscous fluids. In [21] the authors went beyond linearization and considered the effects of shear viscosity on the propagation of nonlinear waves. This study was performed with the help of the well established reductive perturbation method [22][23][24][25].…”