2008.10.9 2008.10.9 SQM’08 SQM’08 1 An explorer for the An explorer for the shear viscosity shear viscosity in the in the formed matter at relativistic heavy ion formed matter at relativistic heavy ion collisions collisions Wu Yuanfang Wu Yuanfang IOPP, Huazhong Normal University, Wuhan, China IOPP, Huazhong Normal University, Wuhan, China 1. 1. Motivation Motivation 2. 2. Azimuthal bin-bin multiplicity Azimuthal bin-bin multiplicity corr. pattern corr. pattern 3. The correlation pattern & shear 3. The correlation pattern & shear viscosity viscosity 4. A rough estimation of 4. A rough estimation of η η in AMPT in AMPT 5. Summary and outlook 5. Summary and outlook Co-authers: Co-authers: Wang Meijuan, Li Lin, and Wang Meijuan, Li Lin, and Liu Lianshou Liu Lianshou Acknowledgements: Acknowledgements: T. Hirano, Li Jiarong, Wang Fuqiang, T. Hirano, Li Jiarong, Wang Fuqiang, Tang Aihong and Xu Nu Tang Aihong and Xu Nu
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Wu Yuanfang IOPP, Huazhong Normal University, Wuhan, China
An explorer for the shear viscosity in the formed matter at relativistic heavy ion collisions. Co-authers: Wang Meijuan, Li Lin, and Liu Lianshou. Acknowledgements: T. Hirano, Li Jiarong, Wang Fuqiang, Tang Aihong and Xu Nu. Motivation Azimuthal bin-bin multiplicity corr. pattern - PowerPoint PPT Presentation
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2008.10.92008.10.9 SQM’08SQM’0811
An explorer for theAn explorer for the shear viscosityshear viscosity in the formed in the formed matter at relativistic heavy ion collisionsmatter at relativistic heavy ion collisions
Wu YuanfangWu YuanfangIOPP, Huazhong Normal University, Wuhan, ChinaIOPP, Huazhong Normal University, Wuhan, China
★ ★ Why not perfect Why not perfect fluid ?fluid ?
★ ★ Why not perfect Why not perfect fluid ?fluid ?
Perfect liquidPerfect liquid Zero viscosityZero viscosity
S. Pratt, S. Pratt, arXiv: 0809.0089arXiv: 0809.0089; S. A. Voloshin, arXiv: 0805.1351.; S. A. Voloshin, arXiv: 0805.1351.
The result of leading order perturbative :The result of leading order perturbative :
for for / 0.8s 0.3s P. Arnold, G. D. Moore and L. G. Yaffe.P. Arnold, G. D. Moore and L. G. Yaffe.
The lower bound of shear viscosity: 1/ 0.08
4s
It reduces the flow values up to 10-30%.
P. Kovtun, D. T. Son, and A. O. Starinets, Phys. Rev. Lett. 94, 111601(2005) .P. Kovtun, D. T. Son, and A. O. Starinets, Phys. Rev. Lett. 94, 111601(2005) .
It is necessary to know the real value of shear viscosity!It is necessary to know the real value of shear viscosity!
★ ★ Main difference between perfect and Main difference between perfect and viscous fluid.viscous fluid.
★ ★ Main difference between perfect and Main difference between perfect and viscous fluid.viscous fluid.
There are friction There are friction between two layers.between two layers.
→→
→→
→→→→→→
→→→→→→→→→→
Perfect liquid:Perfect liquid: →→→→→→→→→→
Viscous liquid:Viscous liquid:
No friction betweenNo friction between
two layers of flow.two layers of flow.
Velocity is const.Velocity is const.
Velocity is different Velocity is different
from layer to layer.from layer to layer.
→→
→→
→→→→→→
The The internal interactioninternal interaction and and velocity gradientvelocity gradient are are directly related to the viscous behavior of the fluid. directly related to the viscous behavior of the fluid.
★ ★ influences of the correlation between N and influences of the correlation between N and vv2 .2 .
Case 5: Randomly produced particles but Case 5: Randomly produced particles but ΦΦ dis. increase with N dis. increase with N
The correlation between N and vThe correlation between N and v22 contributes to the pattern. contributes to the pattern.
It is necessary to study the pattern in fixed N or vIt is necessary to study the pattern in fixed N or v2 2 sample.sample.
2008.10.92008.10.9 SQM’08SQM’0899
3. The correlation pattern and shear viscosity :3. The correlation pattern and shear viscosity : 3. The correlation pattern and shear viscosity :3. The correlation pattern and shear viscosity :
★★ Bin-bin correlation and interaction energyBin-bin correlation and interaction energy★★ Bin-bin correlation and interaction energyBin-bin correlation and interaction energy
( ), 1 ( )IE
IC e E
M. Stephanov, Int. J. Mod. Phys. A20, 4787(2005);M. Stephanov, Int. J. Mod. Phys. A20, 4787(2005);
, is the , is the interaction energyinteraction energy..1
T ( )IE
,,( )Corr I
CE E d d TC d
In the whole system, the total interaction energy is :In the whole system, the total interaction energy is :
If the interaction is small, in the leading order, the correlation is,If the interaction is small, in the leading order, the correlation is,
2008.10.92008.10.9 SQM’08SQM’081010
3. The correlation pattern and shear viscosity :3. The correlation pattern and shear viscosity : 3. The correlation pattern and shear viscosity :3. The correlation pattern and shear viscosity :
★★ Dissipative energy of the fluidDissipative energy of the fluid★★ Dissipative energy of the fluidDissipative energy of the fluid
' 2( )
3i k l l
ik ik ikk i l l
v v v v
x x x x
In hydrodynamics, the viscous stress tensor :In hydrodynamics, the viscous stress tensor :
L. D. Landau & E. M. Lifshitz, Fluid Mechanics, Pergamon Press.L. D. Landau & E. M. Lifshitz, Fluid Mechanics, Pergamon Press.
ηη(p,T) and (p,T) and ξξ(p,T) are shear and bulk viscosity respectively.(p,T) are shear and bulk viscosity respectively.
For incompressible fluid, the dissipative energy is:For incompressible fluid, the dissipative energy is: 2
1
2i k
Dissk i
v vE dVdt
x x
Take the cylindrical coordinates, and assume , Take the cylindrical coordinates, and assume ,
0, 0v
vz
2 2
21 1 1 1
2 2 4T T
Diss
v vE r d dzdt d dzdt
r
2008.10.92008.10.9 SQM’08SQM’081111
3. The correlation pattern and shear viscosity :3. The correlation pattern and shear viscosity : 3. The correlation pattern and shear viscosity :3. The correlation pattern and shear viscosity :
★★ Shear viscosity andShear viscosity and bin-bin correlationbin-bin correlation★★ Shear viscosity andShear viscosity and bin-bin correlationbin-bin correlation
If the bin-bin correlation is only due to viscous interaction, If the bin-bin correlation is only due to viscous interaction,
Then,Then,
Corr DissE Ei.e.,i.e.,
2
,
1
4TvTC d d dzdt
,2
4
T
TC
vdzdt
T T → p→ pTT spectrum; spectrum; → → final velocity gradient.final velocity gradient.2
Tv dzdt
2008.10.92008.10.9 SQM’08SQM’081212
4. A rough estimation of shear viscosity in AMPT:4. A rough estimation of shear viscosity in AMPT: 4. A rough estimation of shear viscosity in AMPT:4. A rough estimation of shear viscosity in AMPT:
★★ Correlation pattern from AMPT with string Correlation pattern from AMPT with string melting:melting:
★★ Correlation pattern from AMPT with string Correlation pattern from AMPT with string melting:melting:
Correlation patternCorrelation pattern
is in-plane like!is in-plane like!
, 0 1 2cos cos(2 )C u u u If we fit it by:If we fit it by:
then :then :5
, 0.0035 6.23*10 cos 0.00049cos(2 )C
For Au + Au collisions at 200 GeV with fixed N and bFor Au + Au collisions at 200 GeV with fixed N and b
2008.10.92008.10.9 SQM’08SQM’081313
4. A rough estimation of shear viscosity in AMPT:4. A rough estimation of shear viscosity in AMPT: 4. A rough estimation of shear viscosity in AMPT:4. A rough estimation of shear viscosity in AMPT:
★★ Velocity Velocity gradient:gradient:
★★ Velocity Velocity gradient:gradient:
If we fit it by:If we fit it by:
then:then:
Velocity gradient Velocity gradient
is in-plane like is in-plane like too!too!
)2cos(cos)( 2102
www
vT
2( ) 4.468 0.0233cos 0.458cos(2 )Tv
2008.10.92008.10.9 SQM’08SQM’081414
4. A rough estimation of shear viscosity in AMPT:4. A rough estimation of shear viscosity in AMPT: 4. A rough estimation of shear viscosity in AMPT:4. A rough estimation of shear viscosity in AMPT:
★★ Shear viscosity in Shear viscosity in AMPT:AMPT:
★★ Shear viscosity in Shear viscosity in AMPT:AMPT:
Take the second harmonics in expansions of correlation Take the second harmonics in expansions of correlation
pattern and velocity gradient, and approximate T=170MeV,pattern and velocity gradient, and approximate T=170MeV,
2 2
2 2
4 cos(2 ) 40.000725
cos(2 )
Tu Tu
w w
It is very small, since the transportation in AMPT It is very small, since the transportation in AMPT
has a very large cross section of scattering.has a very large cross section of scattering.
It is shown recently that the finite interaction range in transportationIt is shown recently that the finite interaction range in transportation
will contribute to the viscous coefficients and conductivity.will contribute to the viscous coefficients and conductivity.S. Cheng & S. Pratt, PRC 65, 024901(2002)S. Cheng & S. Pratt, PRC 65, 024901(2002)
Hans-Joachim Drescher,1 Adrian Dumitru,2 Cl´ement Gombeaud,
and Jean-Yves Ollitrault, PRC 76, 024905(2007)PRC 76, 024905(2007)
2008.10.92008.10.9 SQM’08SQM’081515
5. Summary and outlook5. Summary and outlook
☞ azimuthal bin-bin multiplicity corr. pattern is azimuthal bin-bin multiplicity corr. pattern is suggested.suggested.
☞ Its relation with shear viscosity is demonstrated. Its relation with shear viscosity is demonstrated.
☞ ☞ The shear viscosity inThe shear viscosity in AMPT with string melting isAMPT with string melting is estimated.estimated.
☞☞ The correlation pattern from current and comingThe correlation pattern from current and coming
relativistic heavy ion collisions are looking forward! relativistic heavy ion collisions are looking forward!