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# Extraction of shear viscosity in stationary states of relativistic particle systems

Institut für Theoretische Physik, Johann Wolfgang Goethe-Universität, Max-von-Laue-Strasse 1, DE-60438 Frankfurt am Main, Germany.
(Impact Factor: 2.29). 02/2012; 85(2 Pt 2):026302. DOI: 10.1103/PhysRevE.85.026302
Source: PubMed

ABSTRACT

Starting from a classical picture of shear viscosity we construct a stationary velocity gradient in a microscopic parton cascade. Employing the Navier-Stokes ansatz we extract the shear viscosity coefficient η. For elastic isotropic scatterings we find an excellent agreement with the analytic values. This confirms the applicability of this method. Furthermore, for both elastic and inelastic scatterings with pQCD based cross sections we extract the shear viscosity coefficient η for a pure gluonic system and find a good agreement with already published calculations.

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• "In the past, the numerical solution of the Boltzmann equation was successfully applied to extract the shear viscosity over entropy ratio * Electronic address: greif@th.physik.uni-frankfurt.de η/s [8] [9] [10], as well as the heat conductivity coefficient κ numerically [11]. Heat flow, shear viscosity and bulk viscosity are coefficients that also appear naturally in kinetic theory of single component systems, even without external forces. "
##### Article: Electric Conductivity of the Quark-Gluon Plasma investigated using a pQCD based parton cascade
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ABSTRACT: Electric conductivity is sensitive to effective cross sections among the particles of the partonic medium. We investigate the electric conductivity of a hot plasma of quarks and gluons, solving the relativistic Boltzmann equation. In order to extract this transport coefficient, we employ the Green-Kubo formalism and independently a method motivated by the classical definition of electric conductivity. To this end we evaluate the static electric diffusion current upon influence of an electric field. Both methods give identical results. For the first time, we obtain numerically the Drude electric conductivity formula for an ultrarelativistic gas of quarks and gluons employing constant isotropic binary cross sections. Furthermore we extract the electric conductivity for a system of massless quarks and gluons including $2\leftrightarrow 3$ screened binary pQCD scattering. Comparing with recent lattice results we find an agreement in the temperature dependence of the conductivity.
Preview · Article · Aug 2014 · Physical Review D
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• "Therefore, if one is able to obtain the general form of the solution that such gradients must satisfy in the stationary regime, it would save a huge amount of computational runtime. As already shown in [38], quantities that are conserved in collisions show a linear behavior between the thermal reservoirs. For the boundary conditions implemented in this work, this is realized for the particle density. "
##### Article: Investigation of Heat Conductivity in Relativistic Systems using a Partonic Cascade
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ABSTRACT: Motivated by the classical picture of heat flow we construct a stationary temperature gradient in a relativistic microscopic transport model. Employing the relativistic Navier-Stokes ansatz we extract the heat conductivity {\kappa} for a massless Boltzmann gas using only binary collisions with isotropic cross sections. We compare the numerical results to analytical expressions from different theories and discuss the final results. The directly extracted value for the heat conductivity can be referred to as a literature reference within the numerical uncertainties.
Preview · Article · Jan 2013 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
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##### Article: Calculation of shear viscosity using Green-Kubo relations within a parton cascade
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ABSTRACT: The shear viscosity of a gluon gas is calculated using the Green-Kubo relation. Time correlations of the energy-momentum tensor in thermal equilibrium are extracted from microscopic simulations using a parton cascade solving various Boltzmann collision processes. We find that the pQCD based gluon bremsstrahlung described by Gunion-Bertsch processes significantly lowers the shear viscosity by a factor of 3-8 compared to elastic scatterings. The shear viscosity scales with the coupling as 1/(alpha_s^2\log(1/alpha_s)). For a constant coupling constant the shear viscosity to entropy density ratio has no dependence on temperature. Replacing the pQCD-based collision angle distribution of binary scatterings by an isotropic form decreases the shear viscosity by a factor of 3.
Preview · Article · Jun 2011 · Physical Review C