Properties of the Quantum Fluid at RHIC Strangeness in Quark Matter March 26-31, 2006

Reaction Dynamics t Thermalization Initial stateLiquid stateFreeze-out Expansion, hadronization Pressure-gradient  New phase EoS  Collective flow  Multi Modul Models

Boltzmann transport equation  phase-space distribution Conservation laws: Conservation laws are valid for any distribution f(x,p), however these are not sufficient to determine f(x,p) ! Boltzmann H-theorem: (i) for any f(x,p) the entropy is increasing, (ii)  stationary solution, where the entropy is maximal  local equilibrium and  EoS + P = P (e,n) Solvable for local equilibrium! (0. CE) Realativistic fluid dynamics + η, κ,... Solvable for near local equilibrium too! (1. CE)

Equation of State (EoS) MIT Bag model – highly simplified Lattice QCD -  „Critical Endpoint”, i.e. first order phase trans. (Fodor & Katz)  liquid – gas type of transition Nevertheless, due to the small size of the HI system the fluctuations are large, and so, a direct experimental detection of a sharp transition and the coexistence of two equilibrated phases is not expected. „Soft point” – FD is sensitive to the EoS!

Relativistic fluid dynamics, more detailed: RFD must be used not only for large velocities but for large energies and temperatures also!

Stability, Reynolds number - kinematic viscosity - viscosity - density - length - velocity In an ideal fluid any small perturbation increases and leads to turbulent flow. For stability sufficiently large viscosity and/or heat conductivity are needed! Re  (Calculations are also stabilized by numerical viscosity.) Interesting and important: in RFD detonation fronts are stabilized by radiation and heat conductivity. E.g. : - Rocket propulsion - Implosion, fission- and fusion reactions - Heavy Ion reactions

Preventing turbulence The instability of deflagration- (flame-) front is not desirable at supersonic fronts. With increasing temperature the radiation becomes dominant and stabilizes the flame front.

Re – studies in HICs Theoretical [D. Molnar, U. Heinz, et al., ] η = 50 – 500 MeV/fm 2 c Re  10 – 100 Exp.: 50 – 800 Mev/nucleon energies 80’s [Bonasera, Schurmann, Csernai] scaling analysis of flow parameters. Re  7 – 8 ! (more dilute, more viscous matter) In both cases η/s  1 (0.5 – 5), This is a value large enough to keep the flow laminar in Heavy Ion Collisions !!!

Local equilibrium Fluid components EoS One fluid >>> EoS. Hadronization, chemical FO, kinetic FO Freeze-Out, FO >>> Detectors Reaction dynamics The collective flow shows the features of EoS, if in most of the space-time domain of the reaction the fluid is in local equilibrium !!! M1

Initial state – reaching equilibrium Initial state by V. Magas, L.P. Csernai and D. Strottman Phys. Rev. C64 (01) NexSpherio by F. Grassi, Y. Hama, T. Kodama, B. Tavares M1

„Fire streak” picture – 3 dim. Myers, Gosset, Kapusta, Westfall M1

Flow patterns „Directed Transverse flow” „Elliptic flow” „3 rd flow component” (anti - flow) „Squeeze out”

„3 rd flow” component Hydro [Csernai, HIPAGS’93] [Phys.Lett.B458(99)454] Csernai & Röhrich

FO hypersurface T c =139 MeV M3 [B. Schlei, LANL 2005]

Flow patterns Strong, correlated and dominant “Elliptic”, V 2, flow observed (CERN/BNL). The flow is laminar (η is sufficiently large), & not dissipated (η is sufficiently small) !? V 1, „directed flow” measurements are not as detailed yet. The strong and dominant flow measurements raised large, international attention!

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Origin of the news:

In superstring theory, „based on analogy between black hole physics and equilibrium thermodynamics,... there exist solutions called black branes, which are black holes with translationally invariant horizons.... these solutions can be extended to hydrodynamics,... and black branes possess hydrodynamic characteristics of... fluids: viscosity, diffusion constants, etc.” In this model the authors concluded that η / s = 1 / 4π And then they „speculate” that in general η / s > 1 / 4π vagy η / s > 1. They argue that this is a lower limit especially for such strongly interacting systems where up to now there is no reliable estimate for viscosity, like the QGP. According to the authors the viscosity of QGP must be lower than that of classical fluids.

(Kovtun, et al., PRL 2005) With Kapusta and McLerran we have studied these results and assumptions and found that : - -η vs. T has a typical decreasing and then increasing behaviour, due to classical reasons (Enskog’21) - - η/s has a minimum exactly at the critical point in systems, which have a liquid-gas type of transition - shows a characteristic behaviour in all systems near the critical point (not only in the case of He). - η vs. T shows a characteristic behaviour in all systems near the critical point (not only in the case of He).

Viscosity – Momentum transfer Via VOIDS Via PARTICLES LiquidGas

Helium (NIST) Water (NIST) QGP (Arnold, Moore, Yaffe) This phenomenon can help us to detect experimentally the critical point: η can be determined from (i) fluctuation of flow parameters and from (ii) scaling properties of flow parameters. [Prakash, Venugopalan,.]