Non-equilibrium Dynamics of the Chiral/Deconfinement Phase - PowerPoint PPT Presentation

BLTP seminar, JINR, Dubna, September 27, 2014 Non-equilibrium Dynamics of the Chiral/Deconfinement Phase Transition Igor N. Mishustin Frankfurt Institute for Advanced Studies, J.W. Goethe Universität , Frankfurt am Main and National Research Centre, “ Kurchatov Institute” Moscow

Contents ntents  Introduction: Effects of fast dynamics  Effective potential and fluctuations of order parameter  Chiral fluid dynamics with damping and noise  Extension to finite baryon densities  Dynamical domain formation in 1 st order tansition  Conclusions

Recent cent publi blicat cation ions M. Nahrgang, C. Herold, S. Leupold, I. Mishustin, M. Bleicher, The impact of dissipationand noise on fluctuations in chiral fluid dynamics, J. Phys. G 40 (2013) 055108; C. Herold, M. Nahrgang, I. Mishustin, M. Bleicher, Chiral fluid dynamics with explicit propagation of the Polyakov loop, Phys. Rev. C 87 (2013) 014907; C. Herold, M. Nahrgang, I. Mishustin, M. Bleicher, Formation of droplets with high baryon density at the QCD phase transition in expanding matter, Nucl. Phys. A 925 (2014) 14; I. Mishustin, T. Koide, G. Danicol, G. Torrieri, Dynamics and stability of chiral fluid, Phys. Atom. Nucl. 77, 1130-1144, arXiv:1401.4103.

Phase ase diagr agram am of f str trong ongly ly-inter interact acting ing matter tter -NICA Such a phase diagram is still a beautiful dream! We hope that future FAIR-NICA experiments will help to establish what is the reality.

Eff ffects ects of f fa fast t dynami namics cs Effective thermodynamic potential for a 1 st order transition a b c 2 4 6 a,b,c are functions of ( ; , ) ( , ) T T 0 and T 2 4 6 0 ( ) P Equilibrium is determined by eq 4 cp crossover 1-st order T C T<T c 3 expansion 0 1 2 T=T 3 c spinoidal 4 2 lines 1 H Q T>T c 0 critical line 0 In rapidly expanding system 1-st order transition is delayed until the barrier between two competing phases disappears - spinodal decomposition I. Mishustin, Phys. Rev. Lett. 82 (1999) 4779; Nucl. Phys. A681 (2001) 56

Equ quil ilib ibrium rium fl fluc uctua tuatio tions ns of of or orde der pa param ameter eter in in 1 st st or orde der ph phas ase tr e transi ansition tion ( ) V Probability distribution ( ) exp , P for fluctuations T P( ) P( ) T<T P( ) T>T T=T c c c Phase I Mixed phase Phase II In an equilibrated system fluctuations of the order parameter, i.e. Polyakov loop, should demonstrate bi-modal distributions (lattice calculations?); In a rapidly evolving system these fluctuations will be out of equilibrium; During supercooling process strong fluctuations may develop in the form of droplets of a metastable phase.

Rap apid id ex expa pans nsio ion n th throu ough gh a 1 a 1 st st or orde der ph phas ase e tr tran ansition sition The system is trapped in a metastable state until it enters the spinodal instability region, when Q phase becomes unstable and splits into droplets Csernai&Mishustin, 1995; Mishustin, 1999; Rafelski et al. 2000; Randrup, 2003; Steinheimer&Randrup 2013; …

Evolution of equilibrium fluctuations in 2 nd order phase transition 1 1 2 2 4 ( ) ( ) ( ) , ( ) ( ) a T b a T a T T 0 c 2 2 4 ( ) , a T and 0, , T T T T c c ( ) V Distribution of fluctuations ( ) exp P T T=T T<T T>T c c c 0 0 In rapidly expanding system critical fluctuations have not sufficient time to develop

Critical slowing down in the 2 nd order phase transition Fluctuations of the order parameter evolve according to the relaxation equation ( ) U T>T d eff c dt rel T=T c T=0 In the vicinity of the critical point the relaxation time for the order B parameter diverges - no restoring force 1 ( ) , 2 T rel T T 0 f c (Landau&Lifshitz, vol. X, “ Rolling down” from the top of the potential Physical kinetics) is similar to spinodal decomposition (Csernai&Mishustin 1995)

Critical itical slow owing ing down wn 2 B. Berdnikov, K. Rajagopal, Phys. Rec. D61 (2000) Critical fluctuations have not enough time to build up. One can expect only a factor 2 enhancement in the correlation length even for slow cooling rate, dT/dt=10 MeV/fm.

Simple model for chiral phase transition Scavenius, Mocsy, Mishustin&Rischke, Phys. Rev. C64 (2001) 045202 Linear sigma model (L σ M) with constituent quarks 1 [ ( )] [ ] ( , ), L q i g i q U 5 2 2 2 2 2 2 2 ( , ) ( ) , < > U v H f H f m vac 4 Effective thermodynamic potential Phase diagram contains contributions of mean field σ and quark-antiquark fluid: ( ; , ) ( , ( ; , ) U T U m T eff q 2 2 2 ( ) m g CO, 2 nd and 1 st order chiral transitions are obtained in T- μ plane.

Effective thermodynamic potential 3 2 2 - d p m p ( ; , ) ln 1 exp ( ) , =2 m T T N N f q q c 3 (2 ) T First we consider μ =0 system but tune the order of the chiral phase transition by changing the coupling g.

Equilibrium order parameter field ( ; , ) m T q 2 2 ( ) 0, ( )= g s s 2 U 2 2 2 2 eff s ( ) (3 - ) m g 0 2 1-st order g=4.5 crossover g=3.3 3 solutions at 122 MeV<T<132 MeV Only 1 equilibrium solution at each T unstable states - spinodal instability

Spectrum of plane-wave fluctuations I. Mishustin, T. Koide, G. Danicol, , G. Torrieri, Phys. Atom. Nucl.; arXiv:1401.4103. σ -meson i t ikx ( ) ( , ) x k e excitations 2 2 2 c k Generally two branches: 1) sound branch s 2 2 2 2) sigma branch m k sound waves Solutions with ω 2 <0 T=120 MeV indicate instability T=125 MeV T=131 MeV

Fluctuations in Bjorken background 2 2 ik ( , ) ( ) , - e t z k 2 1 k 2 ( ) ( ) ( ) f T 2 k / s 2 2 ( ) - ( ) s m g s / T T Crossover transition (g=3.3) 1 st order transition (g=4.5)

Non-equilibrium Chiral Fluid Dynamics I.N. Mishustin, O. Scavenius, Phys. Rev. Lett. 83 (1999) 3134; K. Paech, H. Stocker and A. Dumitru, Phys. Rev. C 68 (2003) 044907; M. Nahrgang, C. Herold, S. Leupold, , C. Herold, M. Bleicher, Phys. Rev. C 84 (2011) 024912; M. Nahrgang, C. Herold, S. Leupold, I. Mishustin, M. Bleicher, J. Phys. G40 055108. Fluid is formed by constituent quarks and antiquarks which m g interact with the chiral field via quark effective mass CFD equations are obtained from the energy momentum conservation for the coupled system fluid+field ( ) 0 T T T T S fluid field fluid field U 2 eff ( ) ( ) S g s t We solve generalized e. o. m. with friction ( η ) and noise ( ξ ): Langevin equation U eff g qq t for the order parameter 1 m (f ' ' ' ' ( , ) 0, ( , ) ( , ) ( ) ( )coth 2 t r t r t r m t t r r V T

Calculation of damping term T.Biro and C. Greiner, PRL, 79. 3138 (1997) M. Nahrgang, S. Leupold, C. Herold, M. Bleicher, PRC 84, 024912 (2011) The damping is associated with the processes: , qq It has been calculated using 2PI effective action 3/2 2 m m 2 q 2 2 1 2 g n m F q 2 4 m Around Tc the damping is due to the pion modes, η =2.2/fm

Dynamic simulations: Bjorken-like expansion Initial state: cylinder of length L in z direction, with ellipsoidal cross section in x-y direction 2 z L L At 0: ( ) 0.2 , - ; v 0; 160 t v z c z v T MeV x y 2 2 L Criti tical cal point t (g=3.6 3.63) 3) First st order r (g=5.5 5.5) Mean an value lues s and d standa andard d dev eviati ation on of T T f for r the whole le sys ystem tem and d for r a c centra ntral cell l (1 fm 3 ) ) are re show own as a fu func nction on of ti time. e. Superc ercooling ooling and d rehea eheating ing effec ects ts are e clearly early seen en in the 1-st st order der trans ansitio ition, n, fluct ctuat uation ions s become ecome espec pecial ially ly stron rong g after er 4 fm fm/c. c.

Sigma fluctuations in expanding fireball 2 1 1 [ . dN U 2 2 2 2 2 2 eff | | | | ], , m k m 3 3 k k k k 2 (2 ) 2 d k eq k Critical point (g=3.63) First order (g=5.5) Fluctuat ctuations ions are e rather her weak ak at c cri ritic ical al point nt (lef eft), t), but incr crea ease se stro rongly ngly at the 1 st st order der transi ansition ion (righ right) t) after er 4 fm fm/c

Extension to finite baryon densities C. Herold, M. Nahrgang, I. Mishustin, M. Bleicher, Nucl. Phys. A 925 (2014) 14; Include µ -dependence in Polyakov loop potential,  (cf. Schäfer , Pawlowski, Wambach Fukushima)  Calculate grand canonical potential for finite chemical potential  Propagate (net) baryon density in the hydro sector

Trajectories on the T- μ plane CFD calculations are done for spherical fireball of R=4 fm Isentropic expansion Hydrodynamic evolution  Trajectories are close to isentropes for crossover and CP; Non- equilibrium “back - bending” is clearly seen in FO case;   In the case of strong FO transition (solid lines) the system is trapped in spinodal region for a significant time

Dynamical droplet formation First order Critical point

Splash of a milk drop HEE-NC-57001

Observable signatures of high- density domains High harmonics of baryonic flow Azimuthal fluctuations of net-B (averaged over many events): In single events: strong v n =<cos[n( φ - φ n )]> enhancement at first order PT