Comparisons between hydrodynamics and transport calculations Zhe Xu WPCF, Krakow, Sept. 11, 2008.

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Presentation transcript:

Comparisons between hydrodynamics and transport calculations Zhe Xu WPCF, Krakow, Sept. 11, 2008

Zhe Xu How small is the  /s ? Are there Mach cone shock waves at RHIC ? Motivation

Zhe Xu Outline Transport model Transport vs. viscous and ideal Hydro 1. elliptic flow 2. anisotropy, energy density, temperature 3. shock waves Conclusion

Zhe Xu BAMPS: B oltzmann A pproach of M ulti P arton S catterings A transport algorithm solving the Boltzmann-Equations for on-shell partons with pQCD interactions new development ggg gg (Z)MPC, VNI/BMS, AMPT, PACIAE Elastic scatterings are ineffective in thermalization ! Inelastic interactions are needed ! Transport Model

Zhe Xu Stochastic algorithm P.Danielewicz, G.F.Bertsch, Nucl. Phys. A 533, 712(1991) A.Lang et al., J. Comp. Phys. 106, 391(1993) 3x3x collision rate per unit phase space for incoming particles p 1 and p 2 with  3 p 1 and  3 p 2 : collision probability (Monte Carlo) Space has to be divided into small cells !

Zhe Xu ZX and C. Greiner, PRC 71, (2005) Interaction Probability

Zhe Xu J.F.Gunion, G.F.Bertsch, PRD 25, 746(1982) T.S.Biro at el., PRC 48, 1275 (1993) S.M.Wong, NPA 607, 442 (1996) screened partonic interactions in leading order pQCD screening mass: LPM suppression : the formation time  g : mean free path Gluons freeze out at local energy density = 1 GeV/fm 3.

Zhe Xu Rapidity dependence of total transverse energy ZX, Greiner, Stöcker, PRL 101, , dim. expansion of gluon matter in Au+Au at RHIC

Zhe Xu Elliptic Flow and Shear Viscosity in Au+Au at RHIC 2-3 Parton cascade BAMPS ZX, Greiner, Stöcker, PRL 101, , 2008 viscous hydro. Romatschke, PRL 99, ,2007  /s at RHIC > 0.08 ZX and C.Greiner, PRL 100,2008

Zhe Xu Longitudinal expansion with boost invariance (1+1 dim.) Israel-Stewart hydrodynamics

Zhe Xu P. Huovinen and D. Molnar, arXiv: [nucl-th] for isotropic 2-2 cross sections

Zhe Xu A. El for pQCD 2-2 and 2-3

Zhe Xu A. El

Zhe Xu Shock waves in 1+1 dim. Riemann porblem isotropic 2-2 cross sections I. Bouras Shocks at RHIC ?

Zhe Xu viscous effect

Zhe Xu Comparison to Israel-Stewart Viscous hydro falls to describe the viscous effect in the shock front. I. Bouras and E. Molnar

Zhe Xu 3+1 Dim. expansion at RHIC: pQCD explain large collective flow and small shear viscosity of QCD matter. Initial conditions, hadronization and afterburning are important. 1+1 Dim. with boost invariance: good agreement between parton cascade and IS-hydro in momentum anisotropy, energy density. large difference in fugacity 1+1 Dim. Riemann problem: Parton casacde can describe shock waves, hydro not. Conclusion

Zhe Xu 2-3 Parton cascade BAMPS viscous hydro. Romatschke, PRL 99, ,2007 Hadronization is imporatant !