Shear Viscosity and Viscous Entropy
Production in Hot QGP at Finite Density
报告人： 刘 绘
华中师范大学 粒子所
Perfect fluid ?
•
Well fitted by the
ideal hydrodynamic
model at PT<2GeV.
•
How to understand?
•
Dissipative structures!
PRL89(2002)132301
Elliptic flow v2 as a function of pt for the
strange particles and from minimum-bias
in Au+Au 130GeV collisions.
高能物理年会 桂林（2006）
刘绘 华中师范大学粒子所
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Irreversible thermodynamics & dissipative structure
(

Entropy production

Thermal flux

Energy-momentum tensor
Transport coefficient
Driving force Xij
Intrinsic property
environment
The ratio of transport coefficient
to the entropy production
reflects the driving force
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(
-- transport coefficients)
Evolution of entropy
density
刘绘 华中师范大学粒子所
-- driving force)
Superstring theory in
equilibrium state
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Kinetics theory I
Energy-momentum tensor
fermion
anti-fermion
boson
Correspondingly,
Fluctuation of distribution
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(s: species)
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Kinetics theory II
Boltzmann Equation
two-body scattering amplitude
collision term
Recast the Boltzmann equation
P.Arnold, G.D.Moore and G.Yaffe,
JHEP 0011(00)001
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Shear viscosity
With a definition of inner product and expanded distribution functions,
where
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Collision terms
Performing the integral over dk’ with the help of
Scattering
amplitude
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Distribution function term
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\chi term
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Matrix elements
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•
In Fig. 1(a) and (e), tu/s^2,
the constant 3 and u/s
are not singular, i.e., no
contribution to leading-log.
•
In the approx. 2
s≈-t in t-channel
s≈-u in u-channel
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Distribution functions
N_f is the quark flavor. The factors scaling the distribution functions are the freedom of
degeneration, relevant to the distinguished reaction channels. For example, fermionaitifermion< -- > fermion-antifermion appears 4N_f times in the sum over species
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-functions
Fig.1(b) has two sets of \chi functions because it involves different channels
which bring on different momentum dependence of \chi^q and \chi^g.
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Variational approach
Two-component fucntion
Expand by the same basis
Shear viscosity in this basisset
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Shear viscosity (Nf=2)
Right hand side:
Left hand side:
One function ansatz
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Non-equilibrium entropy density:
viscous process (scheme I)
Entropy density in kinetics theory
With expanded distribution function
Entropy in equilibrium state
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Viscous Entropy production: Scheme I (continued)
Inserting the results from variational approach, the entropy
produced in viscous process becomes
=
Depends on the dynamic parameter fine structure constant , the
thermodynamic parameters T μ and the driving force.
How to understand these dependences?
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Viscous entropy production: Scheme II
Entropy production is
Entropy in non-equilibrium state in local rest frame
Notice
and replace the proper time with the relaxation time
which is solved from the Boltzmann equation
in the relaxation time approximation
the entropy density is:
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Longitudinal evolution
maximum estimation of the velocity gradient
x
u
z
STAR@RHIC,
PRL_91(2003)052303
Notice
Pseudo-rapidity plateau:
With the maximal velocity gradient
Chemical potential
enhances the ratio!
高能物理年会 桂林（2006）
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Discussion on the ratio
Conditions make ratio meaningful:

viscosity/entropy(eq.) >0

Factor > 0
Minimum value
T=181.15MeV
T=126.0MeV
Temperature bound
assume:
When T=181.15MeV, the ratio
has a minimum value of 0.438,
with μ=46MeV
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Summary & Outlook

Shear viscosity of hot QCD at finite temperature has been
calculated in the kinetics theory.

The ratio of viscosity to viscous non-equilibrium entropy density
demonstrates a minimum value and presents a temperature
bound by some physical conditions. Chemical potential enhances
the ratio.

Besides the entropy sources we discussed here, others like
increase of degree of freedom excited by phase transition…might
be also contribute to the entropy production.

The calculation in weakly coupled limit shows that it might be not
sufficient to reproduce the recent experiment data. Strong
coupling or correlation mechanism should be introduced to
explain the experiment.
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Non-equilibrium entropy density:
jet energy loss
Non-equilibrium entropy can be
obtained by reversing the
evolution, i.e.,
All lost energy are converted into
thermal energy
 Even if all the initial energy of jet are converted into thermal
energy, a typical jet contributes 10-3GeV3 to the entropy density in a
volume of 1000fm3
 Uncertainty I: VOLUME
(RHIC: Au+Au 200GeV)
 Uncertainty II: NUMBER OF ‘JETS’ and soft parton energy loss
One, two or many? Not only jets, but also soft parton energy loss!
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