1. Heavy Ion Meeting 2013-10, Inha Univ., Korea, Nov.2, 2013 Tetsufumi Hirano Sophia Univ. K.Murase, TH, arXiv:1304.3243 Y.Tachibana, TH, Nucl.Phys.A904-905(2013)1023c Y.Tachibana, talk at Hard Probes 2013 M.Hongo, Y.Hirono, TH, arXiv:1309.2823 1

2.  Introduction  Relativistic fluctuating hydrodynamics  Medium response to jet propagation  Anomalous hydrodynamics and chiral magnetic effect  Summary 2

3. 0 collision axis time 3. QGP fluid 4. Hadron gas 1. QCD aspects of nuclear structure 2. Non-equilibrium statistical physics 3. Relativistic hydrodynamics 4. Relativistic kinetic theory 1. Color glass condensate 2. Glasma “Form” of matter Approach Hydrodynamics as a central framework of heavy ion collisions 3

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5. Figures adapted from talk by J.Jia (ATLAS) at QM2011 Two particle correlation function is composed solely of higher harmonics 5 See talks by Y.-S.Kim and M.-J. Kweon

6. Most of the people did not believe hydro description of the QGP (~ 1995) Most of the people did not believe hydro description of the QGP (~ 1995) Hydro at work to describe elliptic flow (~ 2001) Hydro at work to describe elliptic flow (~ 2001) E-by-e hydro at work to describe higher harmonics (~ 2010) E-by-e hydro at work to describe higher harmonics (~ 2010) coarsegrainingsize initial profile 6 Is fluctuation important in such a small system?

7. Conventional hydro describes space-time evolution of (coarse-gained) thermodynamic quantities. Conventional hydro describes space-time evolution of (coarse-gained) thermodynamic quantities. Some of microscopic information must be lost through coarse-graining process. Some of microscopic information must be lost through coarse-graining process. Does the lost information play an important role in dynamics on an e-by-e basis? Does the lost information play an important role in dynamics on an e-by-e basis?  Thermal (Hydrodynamic) fluctuation! J.Kapusta, B.Muller, M.Stephanov, PRC85(2012)054906. J.Kapusta, J.M.Torres-Rincon, PRC86(2012)054911. P.Kovtun, G.D.Moore, P.Romatschke, PRD84(2011)025006. J.Peralta-Ramos, E.Calzetta, JHEP1202(2012)085. 7

8. Linear response to thermodynamic force 8 ShearShear stress tensorGradient of flow BulkBulk pressureDivergence of flow DiffusionDiffusion currentGradient of chemical potential

9. 9 Differential form Maxwell-Cattaneo Eq. (simplified Israel-Stewart Eq.) 2. Retarded Green function (causal, 2 nd order hydro) 1. Delta function (acausal, 1 st order hydro)

10. Generalized Langevin Eq. for fields For non-relativistic case, see Landau-Lifshitz, Fluid Mechanics Fluctuation-Dissipation Relation (FDR) K.Murase and TH, arXiv:1304.3243[nucl-th] : Symmetrized correlation function 10 : Hydrodynamic fluctuation

11.  Colored noise!  As a consequence of causality  Note: white noise in differential form K.Murase and TH, arXiv:1304.3243[nucl-th] 11 cf.) C. Young, arXiv:1306.0472

12. Rayleigh-Taylor instability Need numerical implementation of fluctuating hydro Kelvin-Helmhortz instability Figures from J.B.Bell et al., ESAIM 44-5 (2010)1085 12 Ex.) Seeds for instabilities

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14. Figures adapted from talk by C.Roland (CMS) at QM2011 Jet momentum balanced by low p T hadrons outside the jet cone!  Medium response? in-cone out-of-cone 14 See talk by Y.-S. Kim

15. Lost energy  low p T particles at large angle Figure adapted from talk by C.Roland (CMS) at QM2011 15 Horizontal: Jet asymmetry Vertical: Transverse momenta (anti-)parallel to jet axis

16. Jet quenching could affect QGP expansion at LHC (and even at RHIC?) Jet quenching could affect QGP expansion at LHC (and even at RHIC?) Relativistic hydrodynamics with a source term due to propagation of jets Relativistic hydrodynamics with a source term due to propagation of jets 16

17. A 50 GeV jet traverses a background with T=0.5 GeV  Mach-cone like structure Vortex ring behind a jet Y.Tachibana and TH, Nucl.Phys.A904-905(2013)1023c 17

18. Fully non-linear and fully 3D hydro simulation of Mach cone Y.Tachibana and TH, Nucl.Phys.A904-905(2013)1023c 18

19. 19 Energy balance Leading jet Qualitatively consistent with CMS results

20. Jet propagation induces large flow velocity along jet axis. Jet propagation induces large flow velocity along jet axis. How much momentum diffuses perp. to jet axis? How much momentum diffuses perp. to jet axis? 20 Y.Tachibana and TH, Nucl.Phys.A904-905 (2013)1023c Momentum diffusion

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22. Figure taken from http://physics.aps.org/articles/v2/104 Positively charged heavy ion as a source of electro magnetic field  Ampere’s law Magnetic field 22

23. G.Wang (STAR), arXiv:1210.5498 Charge asymmetic results indicate existence of electromagnetic effects of transport? 23

24. Slide taken from a seminar talk by M.Hongo at BNL (2013) D.Kharzeev and H.U.Yee(2011);Y.Burnier et al.(2011) For introduction of CME and CSE, see K.Fukushima, arXiv:1209.5064 chiralseparationeffectchiralmagneticeffect 24

25. Hydrodynamic eqs. under EM fields + anomaly Constitutive eqs. incl. CME and CSE D.T.Son and P.Surowka,PRL103(2009)191601 25

26. 26  Quantum anomaly term

27. Charge density and axial charge density in the transverse plane at 27 M.Hongo, Y.Hirono, TH, arXiv:1309.2823

28. 28 STAR data Need more quantitative analysis of anomalous hydro M.Hongo, Y.Hirono, TH, arXiv:1309.2823

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30. PHOBOS, Phys. Rev. Lett. 98, 242302 (2007) 30

31. B.Alver et al., Phys. Rev. C 77, 014906 (2008) 31

32. 0 collision axis time Finite number of hadrons Propagation of jets Hydrodynamic fluctuation Initial fluctuation and particle production 32

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34. Constitutive equations at Navier-Stokes level thermodynamics force Realistic response Instantaneous response violates causality  Critical issue in relativistic theory  Relaxation plays an essential role 34

35. coarsegraining??? Existence of upper bound in coarse-graining time (or lower bound of frequency) in relativistic theory??? Navier Stokes  causality Non-MarkovianMarkovian Maxwell-Cattaneo 35

36. 36 Numerical implementation in full hydro equation (not linearized one) and its consequences in observables Numerical implementation in full hydro equation (not linearized one) and its consequences in observables Langevin simulation in constrained system? Langevin simulation in constrained system? Dynamic critical phenomena Dynamic critical phenomena  Need further formulation of RFH

37. Jet pair created at off central position Enhancement of low momentum particles at large angle from jet axis out-of-cone  Y.Tachibana and TH, Nucl.Phys.A904-905 (2013)1023c 37

38. Alternative constraint for shear viscosity Alternative constraint for shear viscosity through propagation of jets? Heat-up due to mini-jets propagation similar to neutrino reheating in Super Nova Explosion? Heat-up due to mini-jets propagation similar to neutrino reheating in Super Nova Explosion? Jet propagation momentum transfer perp. to jet propagation 38

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41. M.Hongo, Y.Hirono and TH, arXiv:1309.2823 Backgroundtemperature 41

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