1. Diffusion of transverse correlations and shear viscosity in heavy ion collisions Qun Wang ( 王群 ) Univ of Sci & Tech of China ( 中国科技大学 ) With L.G.Pang,X.N.Wang,R.Xu IWND2009, Shanghai, August 22-25,2009

2. What is shear viscosity shear viscosity = resistance of liquid to shear forces (and hence to flow)

3. Shear viscosity in ideal gas and liquid ideal gas, high T ideal liquid, low T lower bound by uncertainty principle Danielewicz, Gyulassy, 1985 Frenkel, 1955

4. Ratio of Shear Viscosity to entropy density Lacey et al, PRL98, 092301 (2007)

5. Correlation from interaction:example number density momentum correlation Interaction potential

6. Cylindrical coordinate EM tensor for fluid EM conservation of fluid to equation for fluctuation Momentum fluctuation as tool to measure shear viscosity (1) [Gavin, Abdel-Aziz, PRL 2006] local rest frame

7. Diffusion equation for momentum density Diffusion equation for momentum density in rapidity and proper time Momentum fluctuation as tool to measure shear viscosity (2)

8. Momentum fluctuation as tool to measure shear viscosity (3) Correlation of momentum fluctuation Diffusion equation for correlation is broadened by momentum diffusion

9. Momentum fluctuation as tool to measure shear viscosity (4) Connection to observable i labels particles from each event brackets represent the event average Shear viscosity can broaden the rapidity correlations of the momentum current. This broadening can be observed by measuring the transverse momentum covariance as a function of rapidity acceptance.

10. Momentum fluctuation as tool to measure shear viscosity (5) Rapidity correlations to measure the shear viscosity [Gavin, Abdel-Aziz, PRL 2006]

11. Azimuthal correlation in transverse momenta Transverse plane can be separated to -bins Focus on two -bins 1 and 2, define correlation function i,j: particles in bins 1 and 2particle numbers in bins 1 and 2 average is taken over events

12. Diffusion equation for azimuthal correlation in central collisions Cylindrical coordinates, metrics and velocity Diffusion equation for azimutha correlation central collision

13. Diffusion equation for azimuthal correlation in central collisions In the co-moving frame without fluid velocity, diffusion equation is in a simple form with solution

14. Solve diffusion equation in general frame 1. Initial condition given by HIJING 2. Solve fluid equation to determine thermodynamic quantities as input to diffusion equation 3. Average over freeze-out hyper-surface freeze-out energy density

15. Azimuthal correlation in transverse momenta result from HIJING

16. Results for azimuthal correlation (1) Free Gas

17. Results for azimuthal correlation (2) First order phase transition

18. Results for azimuthal correlation (3)

19. Results for azimuthal correlation (4)

20. Results for azimuthal correlation (5)

21. Results for azimuthal correlation (6)

22. Summary and conclusion 1. A diffusion equation for azimuthal correlation for transverse momentum is derived a general Lorentz frame. 2. Mini-jet thermalization is shown in the correlation 3. Azimuthal correaltion as a measure for shear viscosity