Molecular dynamics simulation of strongly coupled QCD plasmas

1. Molecular dynamics simulation of strongly coupled QCD plasmas Péter Hartmann1 Zoltán Donkó1 Gabor J. Kalman2 Péter Lévai3 1 Research Institute for Solid State Physics and Optics of the Hungarian Academy of Sciences H-1525 Budapest, P.O. Box 49 Hungary 2Department of Physics, Boston College Chestnut Hill, MA 02467 USA 3KFKI Research Institute for Particle and Nuclear Physics H-1525 Budapest, P.O. Box 49 Hungary

2. Molecular dynamics simulation of strongly coupled QCD plasmas Outline • Introduction • strongly interacting quark-gluon plasma • classical, strongly coupled, abelian plasmas • The molecular dynamics simulation • potential model for QCD forces • color rotation (random gluon interaction) • Results of the simulation • resonant plasma heating • clusterization, correlation • Results of the model • G plasma coupling parameter

3. Introduction – The quark-gluon plasma Lattice QCD (Fodor, Katz; JHEP 040 (2004) 050): • Latest results: • Cross-over phase transition • Strongly correlated (liquid-like) system • Massive quasi particles sQGP Similar properties to classical, strongly interactingabelian plasma (with large G) The aim of this work is to apply classical strongly coupled plasma physics methods to describe sQGP properties.

4. ions electron background particle densityn particle massm electric chargeQ TemperatureT plasma coupling parameter ion sphere radius plasma frequency Introduction – classical strongly coupled plasmas The simplest system: classical one-component plasma (OCP). OCP: charged heavy particles immersed into a homogeneous neutralizing background. interaction (Coulomb) potential: system parameters: universal parameters: • investigated properties: • structure (pair correlation function, static structure function) • thermodynamics (internal energy, compressibility, equation of state, phase diagram) • transport phenomena (thermal conductivity, shear viscosity, diffusion) • collective dynamics (density and current fluctuations, dispersion relations, instabilities)

5. classical OCP QGP model ions quarks (massive) electron background (neutralizing) gluon background (interacting !!!) Our model Our sQGP model is rooted on the classical OCP model. The links are: • The numerical simulation is based on the classical molecular dynamics scheme: • calculating the forces acting on each particle due to all other particles • integrating the equation of motion for all particles in each time-step • using periodic boundary conditions to handle long range forces • implementing color rotation due to random gluonic interaction

6. +1/3 symmetric (6) - 2/3 antisymmetric (3) potential model for QCD interaction color dependent interaction potential between quark i and j: possible two-quark states (R, G and B are the single-quark color states): color factor:

7. +1/3 with 50% prob. - 2/3 with 50% prob. where D = The interaction matrix Consequences: • equally colored quarks repulse each other • different colors may repulse or attract each other An example: interaction matrix of a 9-quark system (excluding self-interaction and double counting) • quark-gluon interaction: • redistribution of elements D in the interaction matrix (with a characteristic time: tD) • “color rotation”: exchange of colors of some quark pairs (tC)

8. MD results • In the following we present preliminary molecular dynamics results for quark plasma with physicalparameters: • kinetic temperature, T0= 200 MeV • particle density, n = 10 quarks / fm3 • interaction strength, aS = 1 • quark mass, m = 300 MeV • and technical parameters: • number of particles, N = 300 • starting positions= random • initialization time, ti = 106+1dt • measure time, tm = 2x105dt • time-step, dt = 5x10-5 fm • cutoff distance, rcut= 0.1 fm • measured parameters are: • kinetic temperature, T(t) • pair correlation function, g(r)

9. Heating rate depends on tD 1/wp and the color rotation rate: Resonant plasma heating Increase of system temperature appearsdue to the redistribution of the interparticle forces(reassignment of D terms):

10. Clusterization The structural evolution of the system is determined by the time dependence of the interaction (& color rotation) :

11. Correlations More detailed insight into structural properties gives the pair-correlation function – g(r): Using g(r) data solid, liquid and gas structural phases can be identified.

12. OCP [in SI units] quark plasma G= 1.15 default parameters: n = 10 fm-3, T = 200 MeV, aS= 1, C = 1/3 The plasma coupling parameter - G What is the value of G for the quark plasma?

13. Summary • We have presented a possible application of the methodology developed for strongly coupled EM plasmas for the numerical investigation of sQGP. • A quasi-classical implementation of the QCD interaction has been developed. • Simulations were carried out for quark plasma near the critical temperature • energy transfer from the background filed shows a resonance like behavior • structural studies show the tendency of cluster formation • pair correlation functions show the presence of short-range correlations • the plasma coupling parameter G is in the order of unity To do: Lots of exciting research  Discussions with Miklos Gyulassy and the support by grants OTKA T-48389, MTA-OTKA-90/46140, NSF-PHYS-0206695 and DOE-DE-FG02-03ER5471 are gratefully acknowledged.

14. Thank you for your attention!