Presentation is loading. Please wait.

Presentation is loading. Please wait.

2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy Exact results in analytic hydrodynamics UTILIZING THE FLUID NATURE OF QGP M. Csanád, T. Csörg ő, M. I. Nagy.

Published byBeatriz Pear Modified over 10 years ago

Similar presentations

Presentation on theme: "2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy Exact results in analytic hydrodynamics UTILIZING THE FLUID NATURE OF QGP M. Csanád, T. Csörg ő, M. I. Nagy."— Presentation transcript:

1 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy Exact results in analytic hydrodynamics UTILIZING THE FLUID NATURE OF QGP M. Csanád, T. Csörg ő, M. I. Nagy ELTE MTA KFKI RMKI Budapest, Hungary Quark Matter 2008, Jaipur, Rajastan, India February 8, 2008

2 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy High temperature superfluidity at RHIC! All “realistic” hydrodynamic calculations for RHIC fluids to date have assumed zero viscosity  = 0 →  perfect fluid a conjectured quantum limit: P. Kovtun, D.T. Son, A.O. Starinets, hep-th/0405231 How “ordinary” fluids compare to this limit? (4  ) η /s > 10 P. KovtunD.T. SonA.O. Starinetshep-th/0405231 RHIC’s perfect fluid (4  ) η /s ~1 ! T > 2 Terakelvin The hottest & most perfect fluid ever made… (4  R. Lacey et al., Phys.Rev.Lett.98:092301,2007

3 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy Relativistic hydrodynamics Energy-momentum tensor: Relativistic Euler equation: Energy conservation: Charge conservation: Consequence is entropy conservation:

4 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy Context Renowned exact solutions Landau-Khalatnikov solution : dn/dy ~ Gaussian Hwa solution (PRD 10, 2260 (1974)) - Bjorken  0 estimate (1983) Chiu, Sudarshan and Wang: plateaux Baym, Friman, Blaizot, Soyeur and Czyz: finite size parameter  Srivastava, Alam, Chakrabarty, Raha and Sinha: dn/dy ~ Gaussian Revival of interest: Buda-Lund model + exact solutions, Biró, Karpenko+Sinyukov, Pratt (2007), Bialas+Janik+Peschanski, Borsch+Zhdanov (2007) New simple solutions Evaluation of measurables Rapidity distribution Advanced initial energy density HBT radii Advanced life-time estimation

5 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy Goal Need for solutions that are: explicit simple accelerating relativistic realistic / compatible with the data : lattice QCD EoS ellipsoidal symmetry (spectra, v 2, v 4, HBT) finite dn/dy Report on a new class that satisfies these criteria but not simultaneously arXiv:0709.3677v1 [nucl-th] PRC(2008) in press

6 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy Self-similar, ellipsoidal solutions Publication (for example): T. Csörg ő, L.P.Csernai, Y. Hama, T. Kodama, Heavy Ion Phys. A 21 (2004) 73 3D spherically symmetric HUBBLE flow: No acceleration : Define a scaling variable for self-similarly expanding ellipsoids: EoS : (massive) ideal gas Scaling function (s) can be chosen freely. Shear and bulk viscous corrections in NR limit : known analytically.

7 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy New, simple, exact solutions If  = d = 1, general solution is obtained, for initial conditions. It is STABLE ! ARBITRARY initial conditions. It is STABLE ! Possible cases (one row of the table is one solution): Hwa-Bjorken, Buda-Lund type New, accelerating, d dimension d dimensional with p=p( ,  ) (thanks T. S. Biró) Special EoS, but general velocity Nagy,CsT, Csanád: Nagy,CsT, Csanád: arXiv:0709.3677v1

8 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy New simple solutions Different final states from similar initial states are reached by varying

9 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy New simple solutions Similar final states from different initial states are reached by varying

10 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy Rapidity distribution Rapidity distribution from the 1+1 dimensional solution, for  > 1. T f : slope parameter.

11 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy Pseudorapidity distributions BRAHMS data fitted with the analytic formula of Additionally: y  η transformation

12 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy BRAHMS rapidity distribution BRAHMS dn/dy data fitted with the analytic formula

13 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy Advanced energy density estimate Fit result:  > 1 Flows accelerate: do work initial energy density is higher than Bjorken’s Work and acceleration. FYI: For  > 1 (accelerating) flows, both factors > 1

14 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy Advanced energy density estimate Correction depends on timescales, dependence is: With a typical  f /  0 of ~8-10, one gets a correction With a typical  f /  0 of ~8-10, one gets a correction factor of 2!

15 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy Conjecture: EoS dependence of  0 Four constraints 1)  Bj is independent of EoS (  = 1 case) 2) c s 2 = 1 case is solved for any  > 0.5 2) c s 2 = 1 case is solved for any  > 0.5 Corrections due to respect these limits. 3) c s 2 dependence of  is known 4) Numerical hydro results Conjectured formula – given by the principle of Occam’s razor: Using = 1.18, c s = 0.35,  f /  0 = 10, we get c s /  Bj = 2.9 Using = 1.18, c s = 0.35,  f /  0 = 10, we get  c s /  Bj = 2.9 in 200 GeV, 0-5 % Au+Au at RHIC  0 = 14.5 GeV/fm 3 in 200 GeV, 0-5 % Au+Au at RHIC

16 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy Advanced life-time estimate Life-time estimation: for Hwa-Bjorken type of flows Makhlin & Sinyukov, Z. Phys. C 39, 69 (1988) Underestimates lifetime (Renk, CsT, Wiedemann, Pratt, … ) Advanced life-time estimate: width of dn/dy related to acceleration and work At RHIC energies: correction is about +20%

17 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy Conclusions Explicit simple accelerating relativistic hydrodynamics Analytic (approximate) calculation of observables Realistic rapidity distributions; BRAHMS data well described No go theorem: same final states, different initial states New estimate of initial energy density:  c /  Bj ~ 2 @ RHIC dependence on c s estimated,  c /  Bj ~ 3 for c s = 0.35 Estimated work effects on lifetime: ~ 20% increase @ RHIC A lot to do … more general EoS less symmetry, ellipsoidal solutions asymptotically Hubble-like flows

18 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy New simple solutions in 1+D dim Fluid trajectories of the 1+D dimenisonal new solution THANK YOU!

19 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy Back-up Slides

20 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy How Perfect is Perfect? Measure η /s ! Damping (flow, fluctuations, heavy quark motion) ~ η /s FLOW: Has the QCD Critical Point Been Signaled by Observations at RHIC?, R. Lacey et al., Phys.Rev.Lett.98:092301,2007 (nucl-ex/0609025)nucl-ex/0609025 The Centrality dependence of Elliptic flow, the Hydrodynamic Limit, and the Viscosity of Hot QCD, H.-J. Drescher et al., (arXiv:0704.3553)arXiv:0704.3553 FLUCTUATIONS: Measuring Shear Viscosity Using Transverse Momentum Correlations in Relativistic Nuclear Collisions, S. Gavin and M. Abdel-Aziz, Phys.Rev.Lett.97:162302,2006 (nucl-th/0606061)nucl-th/0606061 DRAG, FLOW: Energy Loss and Flow of Heavy Quarks in Au+Au Collisions at √s NN = 200 GeV (PHENIX Collaboration), A. Adare et al., Phys.Rev.Lett.98:172301,2007 (nucl-ex/0611018)nucl-ex/0611018 CHARM!CHARM!

21 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy Landau-Khalatnikov solution Publications: L.D. Landau, Izv. Acad. Nauk SSSR 81 (1953) 51 I.M. Khalatnikov, Zhur. Eksp.Teor.Fiz. 27 (1954) 529 L.D.Landau and S.Z.Belenkij, Usp. Fiz. Nauk 56 (1955) 309 Implicit 1D solution with approx. Gaussian rapidity distribution Basic relations: Unknown variables: Auxiliary function: Expression of is a true „tour de force”

22 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy Landau-Khalatnikov solution Temperature distribution (animation courtesy of T. Kodama) „Tour de force” implicit solution: t=t(T,v), r=r(T,v)

23 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy Hwa-Bjorken solution The Hwa-Bjorken solution / Rindler coordinates

24 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy Hwa-Bjorken solution The Hwa-Bjorken solution / Temperature evolution

25 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy Bialas-Janik-Peschanski solution Publications: A. Bialas, R. Janik, R. Peschanski, arXiv:0706.2108v1 Accelerating, expanding 1D solution interpolates between Landau and Bjorken Generalized Rindler coordinates:

26 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy Hwa-Bjorken solution Publications: R.C. Hwa, Phys. Rev. D10, 2260 (1974) J.D. Bjorken, Phys. Rev. D27, 40(1983) Accelerationless, expanding 1D simple boost-invariant solution Rindler coordinates: Boost-invariance (valid for asymptotically high energies): depends on EoS, e.g.

27 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy New simple solutions in 1+d dim The fluid lines (red) and the pseudo-orthogonal freeze-out surface (black)

28 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy Rapidity distribution Rapidity distribution from the 1+1 dimensional solution, for.

29 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy 1 st milestone: new phenomena Suppression of high p t particle production in Au+Au collisions at RHIC

30 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy 2 nd milestone: new form of matter d+Au: no suppression Its not the nuclear effect on the structure functions Au+Au: new form of matter !

31 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy 3 rd milestone: Top Physics Story 2005 http://arxiv.org/abs/nucl-ex/0410003 PHENIX White Paper: second most cited in nucl-ex during 2006

32 2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy Strange and even charm quarks participate in the flow v 2 for the φ follows that of other mesons v 2 for the D follows that of other mesons 4 th Milestone: A fluid of quarks

Download ppt "2008-02-08M. Csanád, T. Csörg ő, M.I. Nagy Exact results in analytic hydrodynamics UTILIZING THE FLUID NATURE OF QGP M. Csanád, T. Csörg ő, M. I. Nagy."

Similar presentations

M. Csanád at QM’04 Indication for deconfinement at RHIC M. Csanád, T. Csörgő, B. Lörstad and A. Ster (Budapest & Lund) Buda-Lund hydro fits to spectra.

M. Csanád at QM’04 Indication for deconfinement at RHIC M. Csanád, T. Csörgő, B. Lörstad and A. Ster (Budapest & Lund) Buda-Lund hydro fits to spectra.
Further development of the HydroKinetic Model (hHKM) and description of the RHIC and LHC A+A data Yu. M. Sinyukov Bogolyubov Institute for Theoretical.

Further development of the HydroKinetic Model (hHKM) and description of the RHIC and LHC A+A data Yu. M. Sinyukov Bogolyubov Institute for Theoretical.
Mass, Quark-number, Energy Dependence of v 2 and v 4 in Relativistic Nucleus- Nucleus Collisions Yan Lu University of Science and Technology of China Many.

Mass, Quark-number, Energy Dependence of v 2 and v 4 in Relativistic Nucleus- Nucleus Collisions Yan Lu University of Science and Technology of China Many.
R. Lacey, SUNY Stony Brook 1 Arkadij Taranenko Quark Matter 2006 November 13-20, Shanghai, China Nuclear Chemistry Group SUNY Stony Brook, USA PHENIX Studies.

R. Lacey, SUNY Stony Brook 1 Arkadij Taranenko Quark Matter 2006 November 13-20, Shanghai, China Nuclear Chemistry Group SUNY Stony Brook, USA PHENIX Studies.
R. Lacey, SUNY Stony Brook 1 Arkadij Taranenko Helmholtz International Summer School: “Dense Matter In Heavy Ion Collisions and Astrophysics” Dubna, Russia,

R. Lacey, SUNY Stony Brook 1 Arkadij Taranenko Helmholtz International Summer School: “Dense Matter In Heavy Ion Collisions and Astrophysics” Dubna, Russia,
Elliptic flow of thermal photons in Au+Au collisions at 200GeV QNP2009 Beijing, Sep 21 - 26, 2009 F.M. Liu Central China Normal University, China T. Hirano.

Elliptic flow of thermal photons in Au+Au collisions at 200GeV QNP2009 Beijing, Sep , 2009 F.M. Liu Central China Normal University, China T. Hirano.
Supported by DOE 11/22/2011 QGP viscosity at RHIC and LHC energies 1 Huichao Song 宋慧超 Seminar at the Interdisciplinary Center for Theoretical Study, USTC.

Supported by DOE 11/22/2011 QGP viscosity at RHIC and LHC energies 1 Huichao Song 宋慧超 Seminar at the Interdisciplinary Center for Theoretical Study, USTC.
LP. Csernai, Sept. 4, 2001, Palaiseau FR 1 L.P. Csernai, C. Anderlik, V. Magas, D. Strottman.

LP. Csernai, Sept. 4, 2001, Palaiseau FR 1 L.P. Csernai, C. Anderlik, V. Magas, D. Strottman.
Effects of Bulk Viscosity on p T -Spectra and Elliptic Flow Parameter Akihiko Monnai Department of Physics, The University of Tokyo, Japan Collaborator:

Effects of Bulk Viscosity on p T -Spectra and Elliptic Flow Parameter Akihiko Monnai Department of Physics, The University of Tokyo, Japan Collaborator:
R. Lacey, SUNY Stony Brook 1 Arkadij Taranenko Winter Workshop on Nuclear Dynamics Big Sky, MT February 12-17,2007 Nuclear Chemistry Group SUNY Stony Brook,

R. Lacey, SUNY Stony Brook 1 Arkadij Taranenko Winter Workshop on Nuclear Dynamics Big Sky, MT February 12-17,2007 Nuclear Chemistry Group SUNY Stony Brook,
CERN May 30 2007 Heavy Ion Collisions at the LHC Last Call for Predictions Initial conditions and space-time scales in relativistic heavy ion collisions.

CERN May Heavy Ion Collisions at the LHC Last Call for Predictions Initial conditions and space-time scales in relativistic heavy ion collisions.
A. ISMD 2003, Cracow Indication for RHIC M. Csanád, T. Csörgő, B. Lörstad and A. Ster (Budapest & Lund) Buda-Lund hydro fits to.

A. ISMD 2003, Cracow Indication for RHIC M. Csanád, T. Csörgő, B. Lörstad and A. Ster (Budapest & Lund) Buda-Lund hydro fits to.
Marcus Bleicher, WWND 2008 A fully integrated (3+1) dimensional Hydro + Boltzmann Hybrid Approach Marcus Bleicher Institut für Theoretische Physik Goethe.

Marcus Bleicher, WWND 2008 A fully integrated (3+1) dimensional Hydro + Boltzmann Hybrid Approach Marcus Bleicher Institut für Theoretische Physik Goethe.
The Henryk Niewodniczański Institute of Nuclear Physics Polish Academy of Sciences Cracow, Poland Based on paper M.Ch., W. Florkowski nucl-th/0603065 Characteristic.

The Henryk Niewodniczański Institute of Nuclear Physics Polish Academy of Sciences Cracow, Poland Based on paper M.Ch., W. Florkowski nucl-th/ Characteristic.
WWND, San Diego1 Scaling Characteristics of Azimuthal Anisotropy at RHIC Michael Issah SUNY Stony Brook for the PHENIX Collaboration.

WWND, San Diego1 Scaling Characteristics of Azimuthal Anisotropy at RHIC Michael Issah SUNY Stony Brook for the PHENIX Collaboration.
Perfect Fluid: flow measurements are described by ideal hydro Problem: all fluids have some viscosity -- can we measure it? I. Radial flow fluctuations:

Perfect Fluid: flow measurements are described by ideal hydro Problem: all fluids have some viscosity -- can we measure it? I. Radial flow fluctuations:
Perfect Fluid: flow measurements are described by ideal hydro Problem: all fluids have some viscosity -- can we measure it? I. Transverse flow fluctuations:

Perfect Fluid: flow measurements are described by ideal hydro Problem: all fluids have some viscosity -- can we measure it? I. Transverse flow fluctuations:
Effects of Bulk Viscosity at Freezeout Akihiko Monnai Department of Physics, The University of Tokyo Collaborator: Tetsufumi Hirano Nagoya Mini-Workshop.

Effects of Bulk Viscosity at Freezeout Akihiko Monnai Department of Physics, The University of Tokyo Collaborator: Tetsufumi Hirano Nagoya Mini-Workshop.
Viscous hydrodynamics DPF 2009 Huichao Song The Ohio State University Supported by DOE 07/30/2009 July 27-July 31, Detroit, MI with shear and bulk viscosity.

Viscous hydrodynamics DPF 2009 Huichao Song The Ohio State University Supported by DOE 07/30/2009 July 27-July 31, Detroit, MI with shear and bulk viscosity.
Behind QGP Investigating the matter of the early Universe Investigating the matter of the early Universe Is the form of this matter Quark Gluon Plasma?

Behind QGP Investigating the matter of the early Universe Investigating the matter of the early Universe Is the form of this matter Quark Gluon Plasma?

Similar presentations

Ads by Google