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Phase Transitions and the Perfectness of Fluids
Jiunn-Wei Chen
National Taiwan U.
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• Review: shear viscosity, and the minimum bound conjecture
• QCD shear viscosity in the hadronic phase:
(a) zero density (w/ Eiji Nakano)
(b) nuclear L-G phase transition
(w/ Yen-Fu Liu, Yen-Han Li, Eiji Nakano) • Scalar field theory (w/ Mei Huang, Yen-Han Li, Eiji N
akano, Di-Lun Yang)• Bulk Viscosity (w/ Juven Wang)
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• Shear viscosity
.)(3
1
2
)()(
xV
xVxVT ij
ijjiij
y
x
)(yVx
Frictional force
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Shear viscosity measures
how “perfect” a fluid is!
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• Kovtun, Son, and Starinets (’05)
Conjecture: Shear viscosity / entropy density
• Motivated by AdS/CFT
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• QGP (quark gluon plasma) almost saturates the bound @ just above Tc --- a perfect fluid (Teaney; Romatschke, Romatschke; Song, Heinz ), SQGP
• LQCD, gluon pasma (Karsch, Wyld; Nakamura, Sakai; Meyer)
• What happens below Tc?
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QCD Phase Diagram
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• Pion gas ChPT (chiral perturbation theory)
• Non-perturbative in coupling
Boltzman equation
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JWC, Nakano
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QCD Phase Diagram
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The Landscape JWC, Li, Liu, Nakano
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QCD Phase Diagram
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Lacey et al., PRL 98:092301,2007
Cold Unitary Atoms Rupak & Schafer 2007
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of Water
(Lacey et al.)
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2nd-order p.t.:a < 0, b > 0, c = 0 crossover: + No p.t.: a > 0, b > 0, c = 0
1st-order phase transitiona > 0, b < 0, c > 0
(JWC, M. Huang, Y.H. Li, E. Nakana, D.L. Yang)
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• Boltzmann?
• CJT formulism (Cornwall, Jackiw, Tomboulis)
• Mean field calculation
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f
Just one minimum (a < 0)?O(N) model? Large b?
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w/o flavor changing
Invading the bound (I)
(KSS; Cohen; Cherman, Cohen, Hohler)
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Invading the bound (II)
(T. Cohen)
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Invading the bound (III)
Higher derivative gravity (Brigante, Liu, Myers, Shenker, Yaida; Kats, Petrov):
O(1/N) effect could invade the bound.
Could the bound be saved by some consistency requirement (e.g. stability)?
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QCD Bulk Viscosity
Karsch, Kharzeev, Tuchin; Meyer; JWC, Wang
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Outlook
• Universal and behaviors? ( reaches local minimum near p.t. reaches local maximum near p.t.)
• Mapping QCD phase diagram by Locating critical end point (Lacey)
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QCD Phase Diagram
Probing critical end point by (Lacey)
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Outlook
just below Tc for YM
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Question
• Which shear viscosity is bigger? Liquid or gas water near 100 degree C at 1 atm?