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Perfect liquid at RHIC! Problem: all fluids have viscosity.

with Abdel-Aziz in progress. How Can We Measure Viscosity? Sean Gavin Wayne State University. Perfect liquid at RHIC! Problem: all fluids have viscosity. Fundamental question: how big is the viscosity?.

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Perfect liquid at RHIC! Problem: all fluids have viscosity.

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  1. with Abdel-Aziz in progress How Can We Measure Viscosity?Sean Gavin Wayne State University Perfect liquid at RHIC! Problem: all fluids have viscosity. Fundamental question: how big is the viscosity? I. Viscosity and its consequences II. Radial flow fluctuations: Dissipated by shear viscosity III. Contribution to transverse momentum fluctuations

  2. Viscosity viscous contribution to stress tensor, flow velocity v << 1 shear viscosity  resists shear flow vx(z) bulk viscosity  resists expansion “hubble” flow important: typically  << 

  3. How Good is the Perfect Fluid? How can we measure viscosity of parton and hadron fluids? • measure flow through a fixed geometry  elliptic and radial flow; cooling Muronga et al.; Teaney et al.; Heinz, Song & Chaudhuri • fluid response to external probe  jet phenomena, Mach cone Casalderry-Solana, Shuryak & Teaney • attenuation of sound waves  propose:dissipation of fluctuations

  4. Radial Flow Fluctuations average radial flow  vr  small fluctuations u ≈ vr  vr  shear viscosity drives velocity toward the average friction between neighboring radial sheets ask: how can measured fluctuations  viscosity?

  5. z Evolution of Fluctuations u r momentum current: u(z,t) ≈ vr  vr  4-momentum conservation diffusion of small fluctuations + corrections O(R-1) momentum diffusion length shear viscosity  energy density e, pressure P

  6. Viscosity Broadens Rapidity Distribution analogous effect in charge diffusion Stephanov & Shuryak; Abdel-Aziz & Gavin; Koide; Sasaki et al.; Wolchin; Teaney & Moore; Bass, Pratt & Danielowicz viscous diffusion + Bjorken flow random walk in rapidityyvs. proper time V = 2s/0 V momentum diffusion lengths (e+P) formation at0 /0

  7. fluctuations equilibrate by diffusing through volume global equilibrium – diffusion drivesr   Hydrodynamic Momentum Correlations momentum density correlation function equilibrium difference rg rg r g,eqsatisfies diffusion equation Van Kampen, Stochastic Processes in Physics and Chemistry, (Elsevier, 1997); Gardiner, Handbook of Stochastic Methods, (Springer, 2002) width in relative rapidity grows from initial value :

  8. Dynamic Fluctuations Pruneau, Voloshin & S.G. variance minus thermal contribution multiplicityN meanpt correlation function:

  9. ptFluctuations Energy Independent

  10. Hydrodynamic Momentum Correlations pt fluctuations probetransverse momentum density density correlations momentum density correlations observable: measured pt1pt2 plus HIJING R rg and rn are comparable

  11. Abdel-Aziz, S.G - in progress How Much Viscosity? sticky sQGP core + hadronic corona see Hirano & Gyulassy two extreme scenarios: V perfect sticky liquid pQGP ~HRG~ 2 fm perfect liquid sQGP ~ (4 Tc)-1,HRG~ 2 fm  (fm) fluctuations, rapidity window: • Gaussian rg, width  • initial~ 0.25 balance function initial perfect sticky 

  12. Summary multiple scattering phenomena broadens width of rapidity distribution testing the perfect liquid  viscosity info • diffusion coefficient shear viscosity • compare rapidity width of momentum fluctuations for different projectile sizes and energies • cross-check: combine with other indirect viscosity measures schematic calculation -- lots to do: • Maxwell/Muronga type corrections • O(R-1) corrections • angular correlations

  13. Hydrodynamic Density Correlations hydro: stress-energy tensor T and current j number density n = j0 and momentum density gi = T0i phase space density f(x,p)fluctuates: multiplicity fluctuations probedensity density correlation function Measured: NA49; PHENIX; PHOBOS

  14. Hydrodynamic Momentum Correlations pt fluctuations probetransverse momentum density momentum density correlation function observable: measured pt1pt2 plus HIJING R rg and rn are comparable

  15. How Good is the Perfect Fluid? shear viscosity  resists shear flow How can we measure viscosity? • measure flow through a fixed geometry  elliptic and radial flow; cooling Muronga et al.; Teaney et al.; Heinz, Song & Chaudhuri • fluid response to external probe  jet phenomena, Mach cone Casalderry-Solana, Shuryak & Teaney • attenuation of sound waves  propose:dissipation of fluctuations vx(z)

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