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Equation of State and Transport Coefficients of Relativistic Nuclear Matter
Azwinndini Muronga1,2
1Centre for Theoretical Physics & AstrophysicsDepartment of Physics, University of Cape Town
2UCT-CERN Research CentreDepartment of Physics, University of Cape Town
SQM2007
24-29 June 2007, Levoča, Slovakia
Transport properties of relativistic nuclear matter
Viscosities, diffusivities, conductivities.
Determine relaxation to equilibrium in heavy ion collisions – strangeness equilibration (by flavor diffusion), spin and color diffusion
In astrophysical situations such as in neutron stars – cooling and burning of neutron star into a strange quark star
In cosmological applications such as the early universe – electroweak baryogenesis
QED and QCD plasmas
Baym et. al., Gavin, Prakash et. al., Davesne, Heiselberg, Muroya et. al., Muronga, Arnold et. al.,….
Origin of the news:
14-field theory of relativistic dissipative fluid dynamics
Primary variables
Conservation of net charge, energy-momentum and balance of fluxes
qquqqqsuS
CCuqBCuuACP
uFqFuuqFuFuuuFF
uqpuuT
nuN
q
10212
0
012
12121
2
15
12)3(
3
4
633
2)(
02
5
1
4
0
0
0
11211
0
1
2
qqS
CCF
qBCFu
ACFuu
T
Tu
N
q
See A. Muronga, nuc-th/0611090 for details
Relaxation equations for dissipative fluxes
Relaxation equations for the dissipative fluxes
Transport and relaxation times/lengths
q
aT
TTqq
q
q
qqq
q
2
CCCB
TCA q
20
21
22 2
5 , ,16
1100
210
2 , , ,
2 , ,
qqqq
q
TT
T
Transport Coefficients and Relaxation Times/Lengths
Relativistic transport equation
Phase-space integrals
),(),( processes
)( pxIpxFpk
kaa
in out in out
outinnj
n
ijji
ka
jFjjjF
PPppMpdS
pxI
)()()()(
)(2),...,(1
)(),( )4(42
11
4)(
31
0
10
2
Fermions 1
Boltzmann 0
Bosons 1
)(1)(
gA
jFAj
pe
AjF1
)( 00
See A. Muronga, nuc-th/0611091 for details
Transport Coefficients and Relaxation Times/Lengths
For any scalar function of distribution function and any tensor function of momenta
After linearization within relativistic Grad moment method
in out in out
outinnj
n
ijji
jFjjjF
pFdwPPppMpdS
dwppF
)()()()(
)()()(2),...,(1
)(
)()(
')4(42
11
4
)()( 4
100
4
in out
jjFppppWwdC
CuuCCCCuuuuC q 3
1 ,
3
1 ,
cCF
ppxcpxbxapx
jjjFjF
)()()(),(
)()(1)()( 00
Relaxation Coefficients
• Transport coefficients are as important as the equation of state.
• They should be calculated self consistently together with the equation of state.
• The relaxation times/lengths should be compared with the characteristic time/length scales of the system under consideration.
• Strangeness equilibration could be easily understood via strangeness (flavor) diffusion coefficient.
• Looking forward to talks by W. Broniowski and by L. Turko at this meeting.
Looking beyond an idealistic picture
