Motivation

1. Real-time Lattice Simulations of Heavy-Ion Collisions CPIC- Colored Particle In Cell method: The test-particle ansatz allows for a numerical solution of the Vlasov equation and in the collisionless limit leads to Wong's equations: Motivation We study the dynamics of the quark-gluon plasma, as created in heavy-ion collisions using real-time lattice calculations of coupled particle-field systems in classical SU(N) gauge theory. Because occupation numbers are large in the infra-red, the classical field approximation becomes reasonable. Away from the infra-red however, the degrees of freedom should be described by particles. We present first results of real-time simulations of the QCD-Boltzmann-Vlasov equation combining both limits by including the effects of elastic particle collisions and field-particle interactions. We introduce a separation scale, on the particle momentum transfer where is the lattice spacing. Above particles undergo point-like binary scatterings and below scatterings occur via self-consistent field deflections. We demonstrate that in an isotropic plasma particle momentum-space diffusion is independent of the lattice spacing in this scheme. Extending this to anisotropic plasmas we determine the effect of binary collisions on the Chromo-Weibel-instability and study the influence of instabilities on jet broadening. with the coordinates , , and of test particle . is the number of test particles per physical particle. The time evolution of the Yang-Mills field is determined by the standard Hamiltonian method in gauge. In lattice units the Kogut-Susskind Hamiltonian reads: with the number of colors . Inclusion of binary collisions In addition to the field-particle interaction described above, we include elastic particle-particle collisions with momentum exchange above the intermediate scale . The total cross section is calculated from the differential pQCD cross section for the diagrams shown above: Initial setup for the measurement particle-field interaction only For the physically most sensible choice , about 25% of the momentum diffusion is due to particle-field interactions. We find a lattice independent value for for in an SU(2) plasma and with For SU(3) a correction due to a color factor applies. Momentum space diffusion We measure the momentum broadening of hard particles that are placed in a bath of Boltzmann distributed particles and distributed fields, these distributions being the two limits of the Bose-distribution. We set the initial energy density of the fields equal to that in Bose distributed particles up to momentum . As shown on the right this leads to approximate independence of the separation scale in the observable , the average squared transverse momentum gained by the hard particles. particle-field interaction and hard collisions Jet broadening in unstable non-Abelian plasmas For weakly-coupled anisotropic plasmas the local rotational symmetry in momentum space is broken. The fields develop unstable modes, forming configurations where and . This provides a possible explanation for the experimental observation that high-energy jets traversing the plasma perpendicular to the beam axis experience much stronger broadening in rapidity than in azimuth. Growing field components. Weibel-instability and filamentation Star preliminary Au+Au 0-10% Stronger longitudinal broadening: Observed additional near-side long range correlation in . • Conclusion • We extended the CPIC-simulation by hard particle collisions, which lead to • a new kind of parton-cascade including fields and collective phenomena. • Lattice independent results for in an isotropic plasma were determined. • Instabilities in an anisotropic plasma create large domains of strong • chromo-fields that cause stronger broadening of jets in than in . Mechanism of filamentation Current filaments and B-field-domains in the simulation during instability growth. The field configurations during instability growth are such that particles are deflected preferentially in the longitudinal direction (to restore isotropy).