Viscosity at RHIC Scott Pratt & Kerstin Paech Michigan State University QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture. Scott Pratt OUTLINE What is viscosity? Sources of viscosity Bulk viscosity near Tc Scott Pratt
Definition of Viscosity After boosting and rotating, T ( + Txx )vx ( + T )v Txx xx x = 0 ( + Tyy)vy 0
P, B and are functions of Scott Pratt Tzz Definition of Viscosity Txx = P Bv2x vx (2 / 3)v 1 tvx = xTxx + Txx scosity = change in "pressure" to due expansion
lk viscosity = change due to isotropic expansion ear viscosity = change due to anisotropic expansion Scott Pratt Sources of Viscosity 1. If zvz >xvx , 2 pz > 2 px =(4 P / 3)t collision
Vanishes if mean free path -> 0 Scott Pratt Sources of Viscosity 2. If Rinteraction > 0 , P BP 2 Rint coll 2 Rint
coll Important at early times Scott Pratt v2 from Boltzmann Calculation Finiterange effects dampen v2 Scott Pratt S. Cheng, S. P., P. Csizmadia, Y. Nara, D. Molnar, M. Gyulassy, S.E. Vance & B. Zhang, PRC 65, 024901 (2002)
Sources of Viscosity 3. Longitudinal Fields Txx =Tyy = Tzz = Hyper-shear at very early times Increases transverse acceleration Scott Pratt Sources of Viscosity 4. Longitudinal Fields, r =E / 2, E = Ez
Txx = Tyy = 2 Tzz = Hyper-shear for t< 0.5 fm/c Increases transverse acceleration Scott Pratt Sources of Viscosity 5. Chemical non-equilibrium offset from equilibrium dN =(N Nquil) / t cm
dt Nquil N =t cm t (nquil / s) 2 P B= t cm s n s Using some thermodynamics Large when T falls or when m rises Scott Pratt
Sources of Viscosity 6. Mean fields 2 2 + + m ( equil ) = R(t) 2 t t Langevin "force" 2 d x x
m 2 + + k(x xquil) = R (t) t dt k x = x&quil s = 2 &equil m s can blow up at phase transition! Scott Pratt 2 K.Paech & A.Dumitru, PLB 623, 200 (2005) l 2
2 2 2 2 H = (s fp + m p / l ) qs + qurks(T , m = s ) 4 Example: Linear Sigma Model 1st order when g>3.55 Scott Pratt l 4
2 H = s s + s + qurks(T , m = s ) 4 Example: Linear Sigma Model 1st order when g > 3.5549 Scott Pratt Example: Linear Sigma
Model For g=3.4, Txx -> 0 Scott Pratt How might this affect dynamics? P Txx r "traffic jam" flash-like emission Scott Pratt
Rando m Lesso ns 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 Tc Affects dynamics ?? Alternatively, effects can be included throug
Explicit chemical evolution Explicit evolution of fields K.Paech & A.Dumitru, PLB 623, 200 (2005) Scott Pratt Support your local theorist!! http://www.phy.duke.edu/~muller/RTI_Complete.pdf Scott Pratt
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