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Shear Viscosity and Viscous Entropy Production in Hot QGP at Finite Density

Shear Viscosity and Viscous Entropy Production in Hot QGP at Finite Density. 报告人： 刘 绘 华中师范大学 粒子所. Perfect fluid ?. Well fitted by the ideal hydrodynamic model at P T <2GeV. How to understand? Dissipative structures!. PRL89(2002)132301.

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Shear Viscosity and Viscous Entropy Production in Hot QGP at Finite Density

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  1. Shear Viscosity and Viscous Entropy Production in Hot QGP at Finite Density 报告人： 刘 绘 华中师范大学 粒子所

  2. Perfect fluid ? • Well fitted by the ideal hydrodynamic model at PT<2GeV. • How to understand? • Dissipative structures! PRL89(2002)132301 Elliptic flow v2 as a function of pt for the strange particles and from minimum-bias in Au+Au 130GeV collisions. 刘绘 华中师范大学粒子所

  3. ( -- driving force) ( -- transport coefficients) Driving force Xij environment Transport coefficient Intrinsic property Superstring theory in equilibrium state The ratio of transport coefficient to the entropy production reflects the driving force Irreversible thermodynamics & dissipative structure • Entropy production • Thermal flux • Energy-momentum tensor Evolution of entropy density 刘绘 华中师范大学粒子所

  4. Correspondingly, Fluctuation of distribution (s: species) Kinetics theory I Energy-momentum tensor fermion anti-fermion boson 刘绘 华中师范大学粒子所

  5. two-body scattering amplitude collision term Kinetics theory II Boltzmann Equation Recast the Boltzmann equation P.Arnold, G.D.Moore and G.Yaffe, JHEP 0011(00)001 刘绘 华中师范大学粒子所

  6. Shear viscosity With a definition of inner product and expanded distribution functions, where 刘绘 华中师范大学粒子所

  7. Performing the integral over dk’ with the help of Collision terms \chi term Scattering amplitude Distribution function term 刘绘 华中师范大学粒子所

  8. Matrix elements • In Fig. 1(a) and (e), tu/s^2, the constant 3 and u/s are not singular, i.e., no contribution to leading-log. • In the approx. 2 • s≈-t in t-channel • s≈-u in u-channel 刘绘 华中师范大学粒子所

  9. Distribution functions N_f is the quark flavor. The factors scaling the distribution functions are the freedom of degeneration, relevant to the distinguished reaction channels. For example, fermion-aitifermion< -- > fermion-antifermion appears 4N_f times in the sum over species 刘绘 华中师范大学粒子所

  10. -functions Fig.1(b) has two sets of \chi functions because it involves different channels which bring on different momentum dependence of \chi^q and \chi^g. 刘绘 华中师范大学粒子所

  11. Variational approach Two-component fucntion Expand by the same basis Shear viscosity in this basis-set 刘绘 华中师范大学粒子所

  12. Shear viscosity (Nf=2) Right hand side: Left hand side: One function ansatz 刘绘 华中师范大学粒子所

  13. Non-equilibrium entropy density:viscous process (scheme I) Entropy density in kinetics theory With expanded distribution function Entropy in equilibrium state 刘绘 华中师范大学粒子所

  14. = Viscous Entropy production: Scheme I (continued) Inserting the results from variational approach, the entropy produced in viscous process becomes Depends on the dynamic parameter fine structure constant , the thermodynamic parameters T μ and the driving force. How to understand these dependences? 刘绘 华中师范大学粒子所

  15. Viscous entropy production: Scheme II Entropy production is Entropy in non-equilibrium state in local rest frame Notice and replace the proper time with the relaxation time which is solved from the Boltzmann equation in the relaxation time approximation the entropy density is: 刘绘 华中师范大学粒子所

  16. x u z STAR@RHIC, PRL_91(2003)052303 With the maximal velocity gradient Notice Pseudo-rapidity plateau: Longitudinal evolutionmaximum estimation of the velocity gradient Chemical potential enhances the ratio! 刘绘 华中师范大学粒子所

  17. Minimum value T=181.15MeV T=126.0MeV Temperature bound assume: Discussion on the ratio Conditions make ratio meaningful: • viscosity/entropy(eq.) >0 • Factor > 0 When T=181.15MeV, the ratio has a minimum value of 0.438, with μ=46MeV 刘绘 华中师范大学粒子所

  18. Summary & Outlook • Shear viscosity of hot QCD at finite temperature has been calculated in the kinetics theory. • The ratio of viscosity to viscous non-equilibrium entropy density demonstrates a minimum value and presents a temperature bound by some physical conditions. Chemical potential enhances the ratio. • Besides the entropy sources we discussed here, others like increase of degree of freedom excited by phase transition…might be also contribute to the entropy production. • The calculation in weakly coupled limit shows that it might be not sufficient to reproduce the recent experiment data. Strong coupling or correlation mechanism should be introduced to explain the experiment. 刘绘 华中师范大学粒子所

  19. Non-equilibrium entropy can be obtained by reversing the evolution, i.e., All lost energy are converted into thermal energy • Uncertainty I: VOLUME(RHIC: Au+Au 200GeV) Non-equilibrium entropy density:jet energy loss • Even if all the initial energy of jet are converted into thermal energy, a typical jet contributes 10-3GeV3 to the entropy density in a volume of 1000fm3 • Uncertainty II: NUMBER OF ‘JETS’ and soft parton energy loss One, two or many? Not only jets, but also soft parton energy loss! 刘绘 华中师范大学粒子所

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