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

Molecular dynamics simulation of strongly coupled QCD plasmas Peter Hartmann 2 Molecular dynamics simulation of strongly coupled QCD plasmas ● 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 –  plasma coupling parameter Outline

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

Molecular dynamics simulation of strongly coupled QCD plasmas Peter Hartmann 4 electron background ions Introduction – classical strongly coupled plasmas The simplest system: classical one- component plasma (OCP). OCP: charged heavy particles immersed into a homogeneous neutralizing background. system parameters: particle density n particle mass m electric charge Q Temperature T plasma coupling parameter ion sphere radius plasma frequency universal parameters: interaction (Coulomb) potential: 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)

Molecular dynamics simulation of strongly coupled QCD plasmas Peter Hartmann 5 Our model Our sQGP model is rooted on the classical OCP model. The links are: classical OCPQGP model ionsquarks (massive) electron background (neutralizing) gluon background (interacting !!!) 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

Molecular dynamics simulation of strongly coupled QCD plasmas Peter Hartmann 6 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: +1/3 symmetric (6) - 2/3 antisymmetric (3)

Molecular dynamics simulation of strongly coupled QCD plasmas Peter Hartmann 7 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) where D = +1/3 with 50% prob. - 2/3 with 50% prob. quark-gluon interaction: redistribution of elements D in the interaction matrix (with a characteristic time:  D ) “color rotation”: exchange of colors of some quark pairs (  C )

Molecular dynamics simulation of strongly coupled QCD plasmas Peter Hartmann 8 MD results In the following we present preliminary molecular dynamics results for quark plasma with physical parameters: kinetic temperature, T 0 = 200 MeV particle density, n = 10 quarks / fm 3 interaction strength,  S = 1 quark mass, m = 300 MeV and technical parameters: number of particles, N = 300 starting positions = random initialization time, t i = dt measure time, t m = 2x10 5 dt time-step, dt = 5x10 -5 fm cutoff distance, r cut = 0.1 fm measured parameters are: kinetic temperature, T(t) pair correlation function, g(r)

Molecular dynamics simulation of strongly coupled QCD plasmas Peter Hartmann 9 Resonant plasma heating Increase of system temperature appears due to the redistribution of the interparticle forces (reassignment of D terms): Heating rate depends on  D  p and the color rotation rate:

Molecular dynamics simulation of strongly coupled QCD plasmas Peter Hartmann 10 Clusterization The structural evolution of the system is determined by the time dependence of the interaction (& color rotation) :

Molecular dynamics simulation of strongly coupled QCD plasmas Peter Hartmann 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.

Molecular dynamics simulation of strongly coupled QCD plasmas Peter Hartmann 12 The plasma coupling parameter -  What is the value of  for the quark plasma? OCP [in SI units]quark plasma default parameters: n = 10 fm -3, T = 200 MeV,  S  = 1, C = 1/3  = 1.15

Molecular dynamics simulation of strongly coupled QCD plasmas Peter Hartmann 13 Summary Discussions with Miklos Gyulassy and the support by grants OTKA T-48389, MTA-OTKA- 90/46140, NSF-PHYS and DOE-DE-FG02-03ER5471 are gratefully acknowledged. 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  is in the order of unity To do: Lots of exciting research

Molecular dynamics simulation of strongly coupled QCD plasmas Peter Hartmann 14 Thank you for your attention!