Equation of State and Transport Coefficients of Relativistic Nuclear Matter Azwinndini Muronga 1,2 1...
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Transcript of Equation of State and Transport Coefficients of Relativistic Nuclear Matter Azwinndini Muronga 1,2 1...
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