Generalized Entropy and Transport Coefficients of Hadronic Matter Azwinndini Muronga 1,2 1 Centre for Theoretical Physics & Astrophysics Department of Physics, University of Cape Town 2 UCT-CERN Research Centre Department of Physics, University of Cape Town Zimanyi 75 Memorial Workshop
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Generalized Entropy and Transport Coefficients of Hadronic Matter Azwinndini Muronga 1,2 1 Centre for Theoretical Physics & Astrophysics Department of.
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Generalized Entropy and Transport Coefficients of Hadronic 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
Zimanyi 75 Memorial Workshop
02-04 July 2007, Budapest, Hungary
Transport properties of relativistic nuclear matter
Viscosities, diffusivities, conductivities.
Determine relaxation to equilibrium in heavy ion collisions – chemical equilibration (by flavor, 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
Complete fluid dynamics solution requires
- initial conditions - equation of state - transport coefficientsExtract the transport coefficients
and associated time/length scales for a given model of interacting hadrons and/or partons.
Study the sensitivity of the space-time evolution of the system and the calculated distribution of the hadrons to dissipative, non-equilibrium processes
Compare the predicted distribution with those observed in experiments
Baym et. al.; Gavin, Prakash et. al.; Davesne; Heiselberg, Muroya et. al.; Arnold et. al.; AM; Z. Xu and C. Greiner
The interest in shear viscosity to entropy ratio
Energy equation
EoS and Transport coefficients
Temperature evolution
e wher1
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AM, 2002; 2004
Time evolution of thermodynamic quantities
Generalized entropy 4-current
Entropy 4-current:Muller-Israel-Stewart
Entropy density and entropy flux
Entropy production
qquqqqsuS 10212
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1
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See AM, nuc-th/0611090 for details
212
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Relaxation equations for dissipative fluxes
Relaxation equations for the dissipative fluxes
Relaxation times/lengths
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aT
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Fluctuations and Transport Coefficients
Green-Kubo
From generalized entropy
dttqqT
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/1
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tijqji
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Transport Coefficients and Equation of State
From Maxwell-Cattaneo-type equations
Thermodynamics from transport models
Thermodynamics from hadronic gas model (e.g. mesons)
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tT
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Relaxation Coefficients
Shear viscosity and shear relaxation time
AM, 2004;
See also , A. El, C. Greiner and Z. Xu, hep-ph 0706412, using parton model
• Transport coefficients are as important as the equation of state.
• Transport coefficients and relaxation times/lengths probe different time/length scales in fluid dynamics (physics of many scales)
• They should be calculated/extracted 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.
• Knowledge of transport coefficients and associated length/time scales provides good ground for comparison of theoretical prediction with experiments