Transcript PowerPoint Presentation - Kinetic Description of the Final

Properties of the Quantum Fluid at RHIC
Strangeness in Quark Matter
March 26-31, 2006
Reaction Dynamics
Expansion,
hadronization
Thermalization
Initial state
New phase EoS 
Liquid state
Pressure-gradient 
Freeze-out
Collective flow 
Multi Modul Models
t
Realativistic fluid dynamics
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)
+
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
- length
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
- velocity
(Calculations are also stabilized by numerical
viscosity.)
- density
- 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/fm2c 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 !!!
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”
„3rd flow component”
(anti - flow)
„Squeeze out”
„Elliptic flow”
rd
„3
flow” component
Csernai & Röhrich
[Phys.Lett.B458(99)454]
Hydro
[Csernai, HIPAGS’93]
FO hypersurface
Tc=139 MeV
[B. Schlei,
LANL 2005]
M3
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.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)
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
- 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
Liquid
Via
PARTICLES
Gas
[Prakash,
Venugopalan, .]
Helium (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.
Water (NIST)