Dissipative effects from transport and viscous hydrodynamics

Abstract

We compare 2->2 covariant transport theory and causal Israel-Stewart hydrodynamics in 2+1D longitudinally boost invariant geometry with RHIC-like initial conditions and a conformal e = 3p equation of state. The pressure evolution in the center of the collision zone and the final differential elliptic flow v2(pT) from the two theories agree remarkably well for a small shear viscosity to entropy density ratio eta/s ~ 1/(4 pi), and also for a large cross section sigma ~ 50 mb. A key to this agreement is keeping ALL terms in the Israel-Stewart equations of motion. Our results indicate promising prospects for the applicability of Israel-Stewart dissipative hydrodynamics at RHIC, provided the shear viscosity of hot and dense quark-gluon matter is indeed very small for the relevant temperatures T ~ 200-500 MeV.Comment: Presentation at Quark Matter 2008. 4 pages, 3 figure