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Nonequilibrium Dynamics in Astrophysics and Material Science YITP, Kyoto, Japan, Oct. 31-Nov. 3, 2011. Dynamics of Relativistic Heavy Ion Collisions and THE Quark Gluon PlasMA. Tetsufumi Hirano Sophia Univ./ the Univ. of Tokyo. Outline. Introduction Physics of the quark gluon plasma - PowerPoint PPT Presentation
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DYNAMICS OF RELATIVISTIC HEAVY ION COLLISIONS AND THE QUARK GLUON PLASMA
Nonequilibrium Dynamicsin Astrophysics and Material ScienceYITP, Kyoto, Japan, Oct. 31-Nov. 3, 2011
Tetsufumi HiranoSophia Univ./the Univ. of Tokyo
Outline1. Introduction2. Physics of the quark gluon plasma3. Relativistic heavy ion collisions• Elliptic flow• “perfect fluidity”• Higher harmonics
4. Some topics in relativistic hydrodynamics
Introduction• “Condensed” matter physics for
elementary particles• Heavy ion collisions as a
playground of non-equilibrium physics in relativistic system
• Recent findings of the quark gluon plasma and related topics
PHYSICS OF THE QUARK GLUON PLASMA
Two Aspects of Quantum ChromoDynamics
Confinement ofcolor charges
Asymptotic freeof QCD
coupling vs. energy scale
QCD: Theory of strong interaction
What is the Quark Gluon Plasma?
Hadron Gas Quark Gluon Plasma (QGP)
Degree of freedom: Quarks (matter) and gluons (gauge)Mechanics: Quantum ChromoDynamics (QCD)
Low Temperature High
Novel matter under extreme conditions
How High?Suppose “transition” happens whena pion (the lightest hadron) gas is close-packed,𝑛𝜋 ≈
14 𝜋𝑟 𝜋
3
3
≈3.6𝑇 3𝑟 𝜋 ≈0.5 fm
𝑇 𝐶≈100MeV ≈1012K
Note 1: T inside the Sun ~ 107 KNote 2: Tc from the 1st principle calculation ~2x1012 K
Where/When was the QGP?
History of the Universe~ History of form of matter
Micro seconds after Big Bang
Our Universe is filledwith the QGP!
RELATIVISTIC HEAVY ION COLLISIONS
The QGP on the Earth
Front View Side ViewRelativistic heavy ion collisionsTurn kinetic energy (v > 0.99c) into thermal energy
Big Bang vs. Little Bang
Figure adapted fromhttp://www-utap.phys.s.u-tokyo.ac.jp/~sato/index-j.htm
Big Bang vs. Little Bang (contd.)
Big Bang Little BangTime scale 10-5 sec >>
m.f.p./c10-23 sec ~
m.f.p./cExpansion
rate 105-6/sec 1022-23/sec
Spectrum Red shift (CMB) Blue shift (hadrons)
m.f.p. = Mean Free PathNon-trivial issue on thermal equilibration
Non-Equilibrium Aspects of Relativistic Heavy Ion Collisions
0collision axis
time
Au Au
3. QGP fluid
4. hadron gas
1. Entropy production2. Local equilibration
3. Dissipative relativisticfluids
4. Kinetic approachfor relativistic gases
1.2.
Hydrodynamic Simulation of a Au+Au Collision
quark gluon plasma
Time scale ~ 10-22 sec
http://youtu.be/p8_2TczsxjM
Elliptic FlowdN
/df
f0 2p
2v2
~1035Pa Elliptic flow (Ollitrault, ’92)• Momentum
anisotropy as a response to spatial anisotropy
• Known to be sensitive to properties of the system• (Shear) viscosity• Equation of state
2nd harmonics (elliptic flow) Indicator of hydrodynamic behavior
Relativistic Boltzmann Simulations
Zhang-Gyulassy-Ko(’99)
v2 is generated through secondary collisions saturated in the early stage sensitive to cross section (~1/m.f.p.~1/viscosity)
𝜆=1𝜎𝜌 ∝𝜂
l: mean free pathh: shear viscosity
“Hydrodynamic Limit”
𝜀= ⟨ 𝑦2−𝑥2 ⟩⟨𝑦 2+𝑥2 ⟩
Eccentricity xy
𝑣2𝜀 =Momentum Anisotropy
Spatial Anisotropy
Response of the systemreaches “hydrodynamic limit”
vs. transverse particle density
Ideal Hydrodynamics at Work
Au+Au Cu+CuT.Hirano et al. (in preparation)
vs. centrality
Viscous Fluid Simulations
Ratio of shear viscosity to entropy density
(𝜂𝑠 )QGP
=(0.08 0.16 ) ℏ𝑘𝐵≈ 1380 (𝜂𝑠 )
Water≈ 19 (𝜂𝑠 )
Liquid He
vs. transverse particle density
H.Song et al., PRL106, 192301 (2011)
Strong Coupling Nature of the QGP
Large expansion rate of the QGP in relativistic heavy ion collisions
Tiny viscosity when hydrodynamic description of the QGP works in any ways Manifestation of the strong coupling
nature of the QGPNote: Underlying theory Quantum ChromoDynamics (theory of strong interaction)
Event-by-event Fluctuation
Figure adapted from talkby J.Jia (ATLAS) at QM2011
Ideal, but unrealistic?OK on average(?)
Actual collision? Higher
order deformation
Deformation at Higher Order
Dynamical Modeling of Relativistic Heavy Ion Collisions*
0collision axis
time
Au Au
QGP fluid
hadron gas
Relativistic Boltzmann
Relativistic Ideal Hydro
Monte Carlo I.C.
*K.Murase et al. (in preparation)
Deformation in Model Calculations
𝜀𝑛=|⟨𝑟 2𝑒𝑖𝑛 𝜙 ⟩|
⟨𝑟2 ⟩
Sample of entropydensity profile in aplane perpendicularto collision axis
Higher Harmonics from Ideal QGP Fluids
vs. centrality (input) vs. centrality (output)
Response of the QGP to initial deformation roughly scales with
Comparison of vn with Data
Tendency similar to experimental dataAbsolute value Viscosity
Theory Experiment
Impact of Finite Higher Harmonics• Most of people did
not believe hydro description of the QGP (~ 1995)
• Hydro at work to describe elliptic flow (~ 2001)
• Hydro at work (?) to describe higher harmonics (~ 2010)
𝑑≲5 fm
coarsegraining
sizeinitialprofile
𝑑≲1 fm
Thermal Radiation from the QGP
Photon spectra in relativisticheavy ion collisions
Blue shifted spectra with T~200-300 MeV~(2-3)x1012K
RELATIVISTIC HYDRODYNAMICS
Several Non-Trivial Aspects of Relativistic Hydrodynamics
1. Non conservation of particle number nor mass
2. Choice of local rest frame3. Relaxation beyond Fourier,
Fick and Newton laws
Hydrodynamic Equations (Ideal Hydro Case)
, Energy conservation
Momentum conservation,
Charge conservation (net baryon number in QCD),
𝜕𝜇𝑇 𝜇𝜈=0 ,𝜕𝜇𝑁𝜇=0
Several Non-Trivial Aspects of Relativistic Hydrodynamics
1. Non conservation of particle number nor mass
2. Choice of local rest frame3. Relaxation beyond Fourier,
Fick and Newton laws
Choice of Local Rest Frame in Dissipative Fluids1. Charge flow
𝑢𝜇= 1𝑁∑
𝑖
𝑁 𝑖𝜇
𝑛𝑖2. Energy flow (Eigenvector of energy-momentum tensor)
𝑇 𝜇𝜈𝑢𝜈=𝑒𝑢𝜇
Charge diffusion vanishes on
average
No heat flow!
heat flow
chargediffusion
See also talk by Kunihiro
*Energy flow is relevantin heavy ion collisions
Several Non-Trivial Aspects of Relativistic Hydrodynamics
1. Non conservation of particle number nor mass
2. Choice of local rest frame3. Relaxation beyond Fourier,
Fick and Newton laws
Relaxation and CausalityConstitutive equations at Navier-Stokes level
𝑡
thermodynamics force
𝑡 0
𝐹∨𝑅
/𝜅
Realistic response
Instantaneous response violates causality Critical issue in
relativistic theory Relaxation plays an
essential role
See also talk by Kunihiro
𝜏
Causal Hydrodynamics
𝑅 (𝑡 )=∫𝑑𝑡′𝐺𝑅 (𝑡 , 𝑡 ′ )𝐹 ( 𝑡′ )Within linear response
Suppose𝐺𝑅 (𝑡 ,𝑡 ′ )= 𝜅
𝜏 exp(− 𝑡− 𝑡′
𝜏 )𝜃 (𝑡−𝑡 ′)
one obtains differential form�̇� (𝑡 )=− 𝑅 (𝑡 )−𝜅 𝐹 (𝑡 )
𝜏 ,
Maxwell-Cattaneo Eq.
𝑣 signal=√ 𝜅𝜏 <𝑐
Relativistic Fluctuating Hydrodynamics (RFH)
)⟨𝛿𝑅 (𝑥)𝛿 𝑅(𝑥 ′) ⟩≈𝐺(𝑥 ,𝑥 ′)
Thermal fluctuation in event-by-event simulations
dissipative current
thermal noise
thermodynamic force
* In non-relativistic cases, see Landau-Lifshtiz, Fluid Mechanics** Similar to glassy system, polymers, etc?
Fluctuation Dissipation
Coarse-Graining in Time
𝑡
𝐺𝑅
𝑡 ′
𝐺𝑅
𝐺𝑅=𝜅𝜏 𝑒
− 𝑡𝜏 𝐺𝑅≈ 𝜅𝛿 (𝑡 ′ )coarse
graining???
Existence of upper bound in coarse-graining time (or lower bound of frequency) in relativistic theory???
Navier Stokes causality
Non-Markovian Markovian
Maxwell-Cattaneo
𝑡→ 𝑡 ′
Finite Size Effect
𝜉 (𝑥 )∝ 1√∆𝑉
Fluctuation Local volume.
• Information about coarse-grained size?
• Fluctuation term ~ average value? Non-equilibrium small system? Fluctuation would play a crucial
role.• Need to consider (?) finite size
effects in equation of state and transport coefficients
ConclusionPhysics of the quark gluon plasma• Strong coupling nature• Small viscosityPhysics of relativistic heavy ion collisions• Playground of relativistic non-equilibrium system• Relativistic dissipative hydrodynamics• Relativistic kinetic theory• Non-equilibrium field theory