1. Scott Pratt Michigan State University Viscosity at RHIC Scott Pratt & Kerstin Paech Michigan State University

2. Scott Pratt Michigan State University OUTLINE What is viscosity? Sources of viscosity Bulk viscosity near T c

3. Scott Pratt Michigan State University Definition of Viscosity After boosting and rotating, P, B and  are functions of 

4. Scott Pratt Michigan State University Definition of Viscosity Viscosity = change in "pressure" to due expansion Bulk viscosity = change due to isotropic expansion Shear viscosity = change due to anisotropic expansion

5. Scott Pratt Michigan State University Sources of Viscosity 1. If ∂ z v z >∂ x v x, Vanishes if mean free path -> 0

6. Scott Pratt Michigan State University Sources of Viscosity 2. If R interaction > 0, Important at early times

7. Scott Pratt Michigan State University v2 from Boltzmann Calculation Finite-range effects dampen v2 S. Cheng, S. P., P. Csizmadia, Y. Nara, D. Molnar, M. Gyulassy, S.E. Vance & B. Zhang, PRC 65, 024901 (2002)

8. Scott Pratt Michigan State University Sources of Viscosity 3. Longitudinal Fields Hyper-shear at very early times Increases transverse acceleration

9. Scott Pratt Michigan State University Sources of Viscosity 4. Longitudinal Fields, Hyper-shear for  < 0.5 fm/c Increases transverse acceleration

10. Scott Pratt Michigan State University Sources of Viscosity 5. Chemical non-equilibrium Large when T falls or when m rises offset from equilibrium Using some thermodynamics

11. Scott Pratt Michigan State University Sources of Viscosity 6. Mean fields Langevin "force"  can blow up at phase transition!

12. Scott Pratt Michigan State University Example: Linear Sigma Model 1st order when g>3.55 K.Paech & A.Dumitru, PLB 623, 200 (2005)

13. Scott Pratt Michigan State University Example: Linear Sigma Model 1st order when g > 3.5549

14. Scott Pratt Michigan State University Example: Linear Sigma Model For g=3.4, T xx -> 0

15. Scott Pratt Michigan State University How might this affect dynamics? T xx r P "traffic jam" flash-like emission

16. Scott Pratt Michigan State University Rando m Lesson s Numerous sources of viscosity –Finite collision time (shear) –Finite interaction range (shear & bulk) –Longitudinal fields (shear) –Chemical non-equilibrium (bulk) –Non-equilibrium fields (bulk) Shear viscosity important at early times –Affects elliptic flow Bulk viscosity important near T c –Affects dynamics ?? Alternatively, effects can be included through –Explicit chemical evolution –Explicit evolution of fields K.Paech & A.Dumitru, PLB 623, 200 (2005)

17. Scott Pratt Michigan State University Support your local theorist!! http://www.phy.duke.edu/~muller/RTI_Complete.pdf