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Hydrodynamical description of first order phase transitions

Hydrodynamical description of first order phase transitions. Vladimir Skokov (GSI, Darmstadt) in collaboration with D. N. Voskresensky. Special thanks to B. Friman and E. Nakano for discussions. Dense QCD Phases in Heavy Ion Collisions and Supernovae , 11 October, 2009.

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Hydrodynamical description of first order phase transitions

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  1. Hydrodynamical description of first order phase transitions Vladimir Skokov (GSI, Darmstadt) in collaboration with D. N. Voskresensky Special thanks to B. Friman and E. Nakano for discussions Dense QCD Phases in Heavy Ion Collisions and Supernovae, 11 October, 2009 Not diamonds, but just a snapshot of boiling water

  2. Critical dynamics vs meanfield Phase diagram is effectively divided in two parts by the Ginzburg criterion (Gi): 1) region of critical fluctuation 2) region of validity of mean field approximation Critical region Critical dynamics “Conventional” hydrodynamics

  3. Critical dynamics vs mean field I System inside critical region (Gi »1) → development of the critical fluctuations. The relaxation time of long-wave (critical) fluctuations is proportional to the square of the wave-length (in case of H-model the relaxation time τψ~ ξ3). In dynamical processes for successful development of the fluctuation of the system should be inside the critical region for times much longer than the relaxation time of order parameter τ » τψ. In opposite case of fast (expansion) dynamics, the system spends short time near CP (τ « τψ), and the fluctuations are not yet excited. This means that the system is not in full equilibrium, however the equilibrium with the respect to the interaction of neighboring region (short range order) is attained rapidly.

  4. Critical dynamics vs mean field II Including all fluctuations • τ » τψ : • critical fluctuations (fluctuations of transverse momentum, fl. of baryon density, etc.) • sound attenuation (disappearance of Mach cone sin(φ)=cs/v, see Kunihiro et al 2009) • CEP as an attractor of isentropic trajectories (proton/antiproton ration, see Asakawa et al, 2009); but this result under a question mark (Nakano et al, 2009) • etc… τ « τψ: Reestablishment of the mean field dynamics (mean field critical exponents, finite thermal conductivity, shear viscosity, not a Maxwell like construction below CEP, but rather non-monotonous dependence). → The reduction of an observable (by fluctuations) critical temperature (fluctuations will be developed deep in spinodal region).

  5. Critical dynamics vs mean field III τ » τψ:Ideology of critical dynamics: the slowest dynamical mode. thermal mode Model H (can be obtained from non-relativistic hydrodynamics + fast noise + mode-mode coupling) for critical dynamics of liquid-gas CEP (see Eiji Nakano talk): τ « τψor outside critical region Shear and bulk viscosities Eq. for density fluctuations or “sound mode” Eq. for specific entropy fluctuations or “thermal mode” Reference values in vicinity of CEP Eq. for longitudinal and transverse momentum (“shear mode”) current or hydrodynamical velocity. Decouples for fast processes from above two due to absence of mode-mode coupling terms (they are irrelevant for fast processes)

  6. First order phase transition Hydrodynamical equations results in … Eq. for density fluctuations or “sound mode” Eq. for specific entropy fluctuations or “thermal mode” Surface contribution

  7. Hydrodynamics of first order PT Equation of motion for density fluctuations in dimensionless form: Surface tension fluidity of seeds is Control parameters for sound wave damping is

  8. Droplet/bubble evolution R>Rcr R<Rcr droplet bubble Parameters are taken to be corresponded quark-hadron phase transition β ~ 0.02-0.2 (effectively viscous fluidity of seeds), even for conjectured lowest limit for ratio of shear viscosity to entropy density (Tcr –T)/Tcr =0.15; Tcr=162 MeV; L=5 fm; β =0.2

  9. Spinodal instability growing modes oscillating modes see also Randrup, PRC79 (2009) 024601

  10. Spinodal instability Dynamics in spinodal region. Blue – hadrons, Red – quarks.

  11. Conclusion Anomalous fluctuations Collision energy The larger viscosity and the smaller surface tension the effectively more viscous is the fluidity Anomalies in thermal fluctuations near CEP may have not sufficient time to develop Anomalous fluctuation from spinodal region Metastable Spinodal reg. CEP temperature calculated in static models might be significantly higher than the value which may manifest in fluctuations in real HIC Further details in: V.S. and D. Voskresensky, arXiv:0811.3868 snd V.S. and D. Voskresensky, Nucl.Phys.A828:401-438,2009 Dynamical manifestation of anomalous fluctuations

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