Radial flow

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Radial flow

HOLOGRAPHIC THERMALIZATIONNumerics and radial flowWork with Michał Heller, David Mateos, Michał Spalinski, Diego Trancanelli and Miquel TrianaReferences: 1202.0981 (PRL 108) and 1210.xxxxWilke van der ScheeSupervisors: Gleb Arutyunov, Thomas Peitzmann,Koenraad Schalm and Raimond SnellingsPostgrad Encounters on Fundamental Physics, BarcelonaOctober 19, 2012


Outline2/14 Motivation: thermalization of the QGP A simple numerical scheme Radial flow (new results, pictures only)


Elliptic flow: v 23/14 How anisotropic is the final state? Ideal gas/weak coupling Perfect fluid/strong couplingK. Aamodt et al, Elliptic Flow of Charged Particles in Pb-Pb Collisions at √s NN =2.76 TeV (2010)


The geometry4/14In homogeneous case the metric can be:A, B, Σ are functions of r and t B measures anisotropyEinstein’s equations simplify Null coordinates Attractive nature of horizonKey differences with Chesler, Yaffe (2008) are Flat boundary Initial non-vacuum state


5/14Bouncing off the boundary


Interesting features6/14 Always (almost) find fast thermalisation: We tries over 2000 initial states…t iso≤1/T Full evolution is accurately given by quasi-normal modes Easily extended to boost-invariant case Describes longitudinally expanding plasmas


Radial flow7/14 Calculation incorporating longitudinal and radial expansion Numerical scheme very similar to colliding shock-waves: Assume boost-invariance on collision axis Assume rotational symmetry (central collision) 2+1D nested Einstein equations in AdSP.M. Chesler and L.G. Yaffe, Holography and colliding gravitational shock waves in asymptotically AdS 5 spacetime (2010)


Radial flow – initial conditions8/14 Two scales: T and size nucleus Energy density is from Glauber model (~Gaussian) No momentum flow (start at τ ~ 0.05fm/c) Scale solution such thatT = 506 MeV at τ = 0. 6fm/c Metric functions ~ vacuum AdS (not a solution with energy!)H. Niemi, G.S. Denicol, P. Huovinen, E. Molnár and D.H. Rischke, Inuence of the shear viscosity of the quark-gluon plasma on elliptic ow (2011)


9/14Radial flow – results


Radial flow - acceleration10/14 Velocity increases rapidly:3110 g Acceleration is roughly with R size nucleus Small nucleus reaches maximum quickly


Radial flow – energy profile11/14 Energy spreads out:


Radial flow - hydrodynamics12/14 Thermalisation is quick, but viscosity contributes


Radial flow - discussion13/14 Radial velocity at thermalisation was basically unknown Initial condition is slightly ad-hoc, need more physics? We get reasonable pressures Velocity increases consistently in other runs Results are intuitive Input welcome ☺


Conclusion14/14 Numerical scheme provides excellent basis Radial flow, fluctuations, elliptic flow What happens universally? What is the initial state? More fundamental problems: How strong is the coupling? N seems to be large here… Influence of SUSY? Maybe add U(1) or dilaton?

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