Theoretic aspect:Tocalculate Trsp.Coefs.inFTinhighlynontrivial(nonperturbativeladderresummation)(caround5)Cn1g4 lnS9String theory method:Ads/CFT (D.Son etal 2003)/s = 1/4Kinetictheory+uncertaintyprinciple(Gyulassy)1m12元S76
6 Theoretic aspect: • To calculate Trsp. Coefs. in FT in highly nontrivial (nonperturbative ladder resummation) (c around 5) • String theory method: AdS/CFT (D.Son et al 2003) /s = 1/4 . Kinetic theory + uncertainty principle (Gyulassy)
Main obstacle for theoryQCD innonperturbativeregime (T~200Mev)Pertburb. Expansion of QCD is not well behaved for realistic TP/Po1.41.20.892950.63421.52.53.54.55T/T。Forthermodyn.,one can uselattice and resummation techniquesKinetic coefficients are difficult to extract from lattice
7 Main obstacle for theory ◼ QCD in nonperturbative regime (T~200Mev) ◼ Pertburb. Expansion of QCD is not well behaved for realistic T ◼ For thermodyn.,one can use lattice and resummation techniques ◼ Kinetic coefficients are difficult to extract from lattice
Shear ViscosityF3=nA8
8 y v A Fx x = − Shear Viscosity
ViscosityfromKuboformula2Huvdt'ee(t'-t)dadt"Dr(c,a)1088whereDr(c,a') =-io(t-t")<[πi(α,t),πji(α',t")] >Extracting the shear viscosity in momentum space:1 dIm[lim Dr(Q)llgo=0 10 dqoq-0
9 Viscosity from Kubo formula
Nonlinear ResponseS(πμd(,t))9 = n(2) HT23dd70 dqo dqoRe[lim GRi(-Q - Q',Q,Q')]lqo==00-0GR1isa3-pointretardedFCNNonlinear Kubo formula -new result[Carrington,Hou,Kobes,PRD64(2001)03011410
10 Nonlinear Response