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

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Presentation on theme: "Comparisons between hydrodynamics and transport calculations Zhe Xu WPCF, Krakow, Sept. 11, 2008."— Presentation transcript:

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

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

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

4 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

5 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 !

6 Zhe Xu ZX and C. Greiner, PRC 71, 064901 (2005) Interaction Probability

7 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.

8 Zhe Xu Rapidity dependence of total transverse energy ZX, Greiner, Stöcker, PRL 101, 082302, 2008 3+1 dim. expansion of gluon matter in Au+Au at RHIC

9 Zhe Xu Elliptic Flow and Shear Viscosity in Au+Au at RHIC 2-3 Parton cascade BAMPS ZX, Greiner, Stöcker, PRL 101, 082302, 2008 viscous hydro. Romatschke, PRL 99, 172301,2007  /s at RHIC > 0.08 ZX and C.Greiner, PRL 100,2008

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

11 Zhe Xu P. Huovinen and D. Molnar, arXiv:0808.0953 [nucl-th] for isotropic 2-2 cross sections

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

13 Zhe Xu A. El

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

15 Zhe Xu viscous effect

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

17 Zhe Xu 3+1 Dim. expansion at RHIC: pQCD 23 + 32 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

18 Zhe Xu 2-3 Parton cascade BAMPS viscous hydro. Romatschke, PRL 99, 172301,2007 Hadronization is imporatant !

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