shear and bulk viscosities of hot dense matter
DESCRIPTION
Shear and Bulk Viscosities of Hot Dense Matter. Joe Kapusta University of Minnesota. New Results from LHC and RHIC, INT, 25 May 2010. Is the matter created at RHIC a perfect fluid ?. Physics Today, May 2010. Atomic and Molecular Systems. In classical transport theory. and. - PowerPoint PPT PresentationTRANSCRIPT
Shear and Bulk Viscosities of Hot Dense
Matter
Joe Kapusta
University of Minnesota
New Results from LHC and RHIC, INT, 25 May 2010
Is the matter created at RHIC a perfect fluid ?
Physics Today, May 2010
Atomic and Molecular Systems
vTls free~
nl
1~freeIn classical transport theory and
so that as the density and/or cross section is reduced(dilute gas limit) the ratio gets larger.
In a liquid the particles are strongly correlated. Momentumtransport can be thought of as being carried by voids insteadof by particles (Enskog) and the ratio gets larger.
Helium
NIST dataL. Csernai, L. McLerran and J. K.
Nitrogen
NIST dataL. Csernai, L. McLerran and J. K.
OH2
NIST data L. Csernai, L. McLerran and J. K.
2D Yukawa Systemsin the Liquid State
radius Seitz-Wigner1
17parameter coupling Coulomb
at located Minimum
2
2
na
aT
Q
Applications to dusty-plasmas andmany other 2D condensed mattersystems.
Liu & Goree (2005)
QCD• Chiral perturbation theory at low T
(Prakash et al.): grows with decreasing T.
• Quark-gluon plasma at high T (Arnold, Moore, Yaffe): grows with increasing T.
4
4
16
15
T
f
s
)/42.2ln(
12.54 ggs
TT
TT
Tgln2ln
9
4ln
8
9
)(
1222
MeV 30T
QCDLow T (Prakash et al.)using experimentaldata for 2-bodyinteractions.
High T (Yaffe et al.)using perturbativeQCD.
L. Csernai, L. McLerran and J. K.
Shear vs. Bulk Viscosity
Shear viscosity is relevant for change in shape at constant volume.
Bulk viscosity is relevant for change in volume at constant shape.
Bulk viscosity is zero for point particles and for a radiationequation of state. It is generally small unless internal degreesof freedom (rotation, vibration) can easily be excited incollisions. But this is exactly the case for a resonance gas –expect bulk viscosity to be large near the critical temperature!
Lennard-Jones potential
Meier, Laesecke, KabelacJ. Chem. Phys. (2005)
Pressure fluctuations give peak in bulk viscosity.
QCD• Chiral perturbation theory at low T
(Chen, Wang): grows with increasing T.
• Quark-gluon plasma at high T (Arnold, Dogan, Moore, ): decreases with increasing T.
4
4
2 8
3ln
4
1ln
8
9
f
T
TTspp
)/34.6ln(5000
4
g
g
s
TT
TT
Tgln2ln
9
4ln
8
9
)(
1222
MeV 30T
QCDLow T (Chen & Wang)using chiral perturbation theory.
High T (Arnold et al.)using perturbativeQCD.
ς/s rises dramatically as Tc is approached from above (Karsch, Kharzeev, Tuchin) Lattice w/o quarks (Meyer) → 0.008 at T/Tc=1.65 and 0.065 at T/Tc=1.24
QCDLow T (Prakash et al.) using experimentaldata for 2-bodyinteractions.
High T (Arnold et al.)using perturbativeQCD.
ς/s rises dramatically as Tc is approached from above (Karsch, Kharzeev, Tuchin) Lattice w/o quarks (Meyer) → 0.008 at T/Tc=1.65 and 0.065 at T/Tc=1.24
Quasi-Particle Theory of Shear and Bulk Viscosity of Hadronic Matter
• Relativistic• Allows for an arbitrary number of hadron species• Allows for arbitrary elastic and inelastic collisions• Respects detailed balance• Allows for temperature-dependent mean fields
and quasi-particle masses• The viscosities and equation of state are
consistent in the sense that the same interactions are used to compute them.
P. Chakraborty & J. K.
P. Chakraborty & J. K.
Linear Sigma Model
MeV 600m MeV 900m
Calculated in the self-consistent Phi-derivable approximation= summation of daisy + superdaisy diagrams= mean field plus fluctuations
v
Go beyond the mean field approximation by averagingover the thermal fluctuations of the quasi-particles asindicated by the angular brackets.
1
1
)2(32
1
1
)2(2
0
2
1
2
1)(
/
2
3
3
22
/
2
3
3
22
2
22
2
22
2222
TE
TE
eE
ppd
m
eE
ppd
m
v
UUm
Um
mmUT
mean field fluctuation
P. Chakraborty & J. K.
Linear Sigma Model
MeV 600m MeV 900m
P. Chakraborty & J. K.
Linear Sigma Model
Solution to the integral equation:
P. Chakraborty & J. K.
Linear Sigma Model
a
aeqaaa
a
TEfEE
ppd
T)/()(
)2(15
12
4
3
3
Relaxation time approximation
P. Chakraborty & J. K.
Linear Sigma Model
Increasing the vacuum sigma mass causes the crossovertransition to look more like a second order transition.
P. Chakraborty & J. K.
Linear Sigma Model
a
aassa
eqa
a
aa
Td
mdTmvpvTEf
E
Epd
T
2
2
222222
31
23
3
)/()(
)2(
1
Violation of conformality
P. Chakraborty & J. K.
Linear Sigma Model
a
aassa
eqa
a
aa
Td
mdTmvpvTEf
E
Epd
T
2
2
222222
31
23
3
)/()(
)2(
1
Violation of conformality
Romatschkes 2007
and /sBoth
Both η/s and ζ/s depend on T – they are not constant.Beam energy scans at RHIC and LHC are necessaryto infer their temperature dependence.
Conclusion
• Hadron/quark-gluon matter should have a minimum in shear viscosity and a maximum in bulk viscosity at or near the critical or crossover point in the phase diagram analogous to atomic and molecular systems.
• Sufficiently detailed calculations and experiments ought to allow us to infer the viscosity/entropy ratios. This are interesting dimensionless measures of dissipation relative to disorder.
Conclusion
• RHIC and LHC are thermometers (hadron ratios, photon and lepton pair production)
• RHIC and LHC are barometers (elliptic flow, transverse flow)
• RHIC and LHC are viscometers (deviations from ideal fluid flow)
• There is plenty of work for theorists and experimentalists!