Shear viscosity and out of equilibrium dynamics

Abstract

Using Grad's method, we calculate the entropy production and derive a formula for the secondorder shear viscosity coefficient in a one-dimensionally expanding particle system, which can also be considered out of chemical equilibrium. For a one-dimensional expansion of gluon matter with Bjorken boost invariance, the shear tensor and the shear viscosity to entropy density ratio η/s are numerically calculated by an iterative and self-consistent prescription within the second-order Israel-Stewart hydrodynamics and by a microscopic parton cascade transport theory. Compared with η/s obtained using the Navier-Stokes approximation, the present result is about 20% larger at a QCD coupling α s ∼ 0.3(with η/s ≈ 0.18) and is a factor of 2 − 3 larger at a small coupling α s ∼ 0.01. We demonstrate an agreement between the viscous hydrodynamic calculations and the microscopic transport results on η/s, except when employing a small α s . On the other hand, we demonstrate that for such small α s , the gluon system is far from kinetic and chemical equilibrium, which indicates the break down of second-order hydrodynamics because of the strong noneqilibrium evolution. In addition, for large α s (0.3 − 0.6), the Israel-Stewart hydrodynamics formally breaks down at large momentum p T > ∼ 3 GeV but is still a reasonably good approximation.

Shear and bulk viscosities of the gluon plasma in a quasiparticle description

“…Moreover, within a parton cascade model based on kinetic theory [81], a value for η/s ∼ 0.5 was found [82], which is much smaller than the pQCD result η/s ∼ 2.7 [75,76] at comparable coupling α s ∼ 0.1. Recent similar studies report η/s ∼ 0.8 [83] and η/s ∼ 1 [84,85] instead.…”

A relativistic dissipative hydrodynamic description for systems including particle number changing processes

“…The relation between the (transport) collision rate and the shear viscosity coefficient was reported in Refs. [21,32]. Here we use the formula derived in [21] η = − π µν π µν 2T C 0 π µν P µν (20) with…”

“…The dynamical behaviour of a particle system resembles the one described by viscous hydrodynamics if the particle mean free path is much smaller than macroscopic scales. Comparisons between hydrodynamic and transport calculations are always useful to examine the applicability limits of viscous hydrodynamic theories [9,21,22,24,25].…”

“…The QGP is considered to possess a constant η/s value during its evolution. Different from the previous studies of chemical equilibration of the QGP basing on either ideal [10,11] or first-order [20] hydrodynamic equations, we apply the second-order Israel-Stewart [9,21] as well as the extended third-order hydrodynamic equations [22] to describe the QGP evolution. The hydrodynamic equations are now coupled with a rate equation for the particle number density.…”

“…[9,21,22,24,25]. The η/s is extracted from the BAMPS calculations using the procedure introduced by us in Ref.…”