Hydrodynamic Instability in the QuarkGluon Plasma

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Hydrodynamic Instabilityin the Quark-Gluon Plasma

• Carlos E. Aguiar
• Instituto de Física - UFRJ

C.E.A., E.S. Fraga, T. Kodama, nucl-th/0306041
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• Outline
• Introduction explosive hadronization
• Thermodynamics of the chiral phase transition
• Supercooling and spinodal decomposition
• Hydrodynamics of the chiral phase transition
• Fluid mechanical instability in the QGP
• Comments

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Heavy Ion Collisions at High Energies
Au
Au
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Heavy Ion Collisions at High Energies
mixedphase
QGP
SPH calculation
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Explosive Hadronization?
___ strong 1st order ...... weak 1st order - - -
crossover D. Zschiesche et al. Phys. Rev. C 65
(2002) 064902

• HBT radii

sudden emission
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The Phase Diagram of Strongly Interacting Matter
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Lattice QCD and Freezeout States
Z. Fodor and S. D. Katz, Phys. Lett. B 534
(2002) 87, JHEP 0203 (2002) 014
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Thermodynamics of theChiral Phase Transition
Linear sigma model
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Partition function
Effective potential

• mean field approximation ? ? lt?gt

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Effective Potential
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Supercooling and Spinodal Decomposition
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Pressure and Chiral Field
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Mesons
First order
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Pressure and Chiral Field
Crossover
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Mesons
Crossover
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Chiral Phase Diagram
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T-n Diagram
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Hydrodynamics of the Chiral Phase Transition
Action
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Chiral Hydrodynamics
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Wave Motion
Perturbation ofequilibrium
Linearizedequations
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Chiral and Sound Modes
Dispersion relation
Long wavelengths
sound waves
chiral waves
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Hydrodynamic Instability
If
then ?s2 lt 0, and the sound modes become
unstable, growing exponentially instead of
propagating. This instability occurs before the
chiral spinodal line (m?2 0) is reached. More
importantly, the crossover region (m?2 ? 0) is
unstable.
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Hydrodynamic Instability in the QGP
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Instability Line in the T-n Plane
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• In summary
• The nonequilibrium chiral condensate changes
  qualitatively the hydrodynamical behavior of
  the QGP
• Explosive hadronization doesnt need spinodal
  decomposition, and can occur even in the
  crossover region.

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• Final comments
• This is a very general effect it doesnt depend
  on specific aspects of the sigma model.
• The instability develops even for very slow
  cooling, contrary to spinodal decomposition.
• Finite size effects may be important in nuclei
  ?min 5 fm at the critical point
• Implications for the hadronization process in
• heavy ion collisions (?)
• early universe (!)