Folie 1

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

• How small is the h/s ?
• Are there Mach cone shock waves at RHIC ?

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Outline

• Transport model
• Transport vs. viscous and ideal Hydro
• elliptic flow
• anisotropy, energy density, temperature
• shock waves
• Conclusion

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Transport Model
BAMPS Boltzmann Approach of MultiParton
Scatterings 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 !
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Stochastic algorithm
P.Danielewicz, G.F.Bertsch, Nucl. Phys. A 533,
712(1991) A.Lang et al., J. Comp. Phys. 106,
391(1993)
Space has to be divided into small cells !
D3x
collision rate per unit phase space for
incoming particles p1 and p2 with D3p1 and D3p2
collision probability (Monte Carlo)
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Interaction Probability
ZX and C. Greiner, PRC 71, 064901 (2005)
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screened partonic interactions in leading order
pQCD
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)
screening mass
LPM suppression the formation time
Lg mean free path
Gluons freeze out at local energy density 1
GeV/fm3.
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31 dim. expansion of gluon matter in AuAu at
RHIC
Rapidity dependence of total transverse energy
ZX, Greiner, Stöcker, PRL 101, 082302, 2008
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Elliptic Flow and Shear Viscosity in AuAu at RHIC
viscous hydro. Romatschke, PRL 99, 172301,2007
2-3 Parton cascade BAMPS ZX,
Greiner, Stöcker, PRL 101, 082302, 2008
h/s at RHIC gt 0.08
ZX and C.Greiner, PRL 100,2008
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Longitudinal expansion with boost invariance (11
dim.)
Israel-Stewart hydrodynamics
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P. Huovinen and D. Molnar, arXiv0808.0953
nucl-th
for isotropic 2-2 cross sections
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A. El
for pQCD 2-2 and 2-3
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A. El
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Shock waves in 11 dim. Riemann porblem
isotropic 2-2 cross sections
I. Bouras
Shocks at RHIC ?
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viscous effect
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Comparison to Israel-Stewart
I. Bouras and E. Molnar
Viscous hydro falls to describe the viscous
effect in the shock front.
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Conclusion

• 31 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 .
• 11 Dim. with boost invariance
• good agreement between parton cascade and
  IS-hydro in momentum anisotropy, energy density.
• large difference in fugacity
• 11 Dim. Riemann problem
• Parton casacde can describe shock waves,
  hydro not.

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