Properties of the Quantum Fluid at RHIC

Strangeness in Quark MatterMarch 26-31, 2006

Reaction Dynamics

t

Thermalization

Initial state Liquid state Freeze-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 1000 - 2000

(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., ] Theoretical [D. Molnar, U. Heinz, et al., ] ηη = 50 – 500 MeV/fm = 50 – 500 MeV/fm22c Re c Re 10 – 100 10 – 100

Exp.: 50 – 800 Mev/nucleon energies 80’sExp.: 50 – 800 Mev/nucleon energies 80’s[Bonasera, Schurmann, Csernai] [Bonasera, Schurmann, Csernai] scaling analysis of flow parameters. scaling analysis of flow parameters. Re Re 7 – 8 ! 7 – 8 !(more dilute, more viscous matter)(more dilute, more viscous matter)

In both cases In both cases ηη/s /s 1 (0.5 – 5) , 1 (0.5 – 5) ,This is a value large enough to keep the This is a value large enough to keep the flow laminar in Heavy Ion Collisions !!!flow laminar in Heavy Ion Collisions !!!

Initial state – reaching equilibrium

Initial state by V. Magas, L.P. Csernai and D. Strottman Phys. Rev. C64 (01) 014901

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”

„3rd flow component”(anti - flow)

„Squeeze out”

„3rd flow” component

Hydro

[Csernai, HIPAGS’93]

[Phys.Lett.B458(99)454]Csernai & Röhrich

FO hypersurface Tc=139 MeV

M3

[B. Schlei, LANL 2005]

Flow patterns• Strong, correlated and dominant “Elliptic”,

V2, flow observed (CERN/BNL).• The flow is laminar (η is sufficiently large),

& not dissipated (η is sufficiently small) !?• V1, „directed flow” measurements are not

as detailed yet.• The strong and dominant flow

measurements raised large, international attention!

origo.huorigo.hu

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)

WithWith KapustaKapusta andand McLerran McLerran we we have studied these results and have studied these results and assumptions and found that :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

- η vs. T shows a characteristic shows a characteristic behaviour in behaviour in allall systems near the systems near the critical point (not only in the case of critical point (not only in the case of He).He).

Viscosity – Momentum transferVia VOIDSVia VOIDS Via PARTICLESVia PARTICLES

LiquidLiquid GasGas

Helium (NIST)

Water (NIST)

QGP (Arnold, Moore, Yaffe)

This phenomenon can help us This phenomenon can help us to detect experimentally the to detect experimentally the critical point:critical point:

η can be determined from (i) fluctuation of flow parameters and from (ii) scaling properties of flow parameters.

[Prakash, Venugopalan, .]