Towards a full solution of relativistic Boltzmann equation for quark-gluon matter on GPUs

Abstract

We have developed a numerical framework for a full solution of the relativistic Boltzmann equations for the quark-gluon matter using the multiple Graphics Processing Units (GPUs) on distributed clusters. Including all the $2\to 2$ scattering processes of 3-flavor quarks and gluons, we compute the time evolution of distribution functions in both coordinate and momentum spaces for the cases of pure gluons, quarks and the mixture of quarks and gluons. By introducing a symmetrical sampling method on GPUs which ensures the particle number conservation, our framework is able to perform the space-time evolution of quark-gluon system towards thermal equilibrium with high performance. We also observe that the gluons naturally accumulate in the soft region at the early time, which may indicate the gluon condensation.

arXiv comment32 pages, 12 figures

References in corpus (72)

• Computing Quark and Gluon Distribution Functions for Very Large Nuclei
• The Color Glass Condensate
• The Intrinsic Glue Distribution at Very Small x
• Bottom-up thermalization in heavy ion collisions
• Solving Lattice QCD systems of equations using mixed precision solvers on GPUs
• Some Features of the Glasma
• ZPC 1.0.1: a parton cascade for ultrarelativistic heavy ion collisions
• Thermalization of gluons in ultrarelativistic heavy ion collisions by including three-body interactions in a parton cascade
• Hydrodynamic Transport Coefficients in Relativistic Scalar Field Theory
• Effective Kinetic Theory for High Temperature Gauge Theories
• Gluon Production from Non-Abelian Weizsäcker-Williams Fields in Nucleus-Nucleus Collisions
• Gluon Production at High Transverse Momentum in the McLerran-Venugopalan Model of Nuclear Structure Functions
• The initial energy density of gluons produced in very high energy nuclear collisions
• Early thermalization at RHIC
• Scaling of transverse energies and multiplicities with atomic number and energy in ultrarelativistic nuclear collisions
• Production of gluons in the classical field model for heavy ion collisions
• Isotropization and hydrodynamization in weakly coupled heavy-ion collisions
• QCD Plasma Instabilities and Bottom-Up Thermalization
• Collective modes of an Anisotropic Quark-Gluon Plasma II
• Coherent gluon production in very high energy heavy ion collisions
• Pseudorapidity distribution and decorrelation of anisotropic flow within CLVisc hydrodynamics
• Toward Equilibration in the Early Stages After a High Energy Heavy Ion Collision
• Color Glass Condensate and Glasma
• Lattice Boltzmann scheme for relativistic fluids
• Sailfish: a flexible multi-GPU implementation of the lattice Boltzmann method
• Chromodynamic Weibel instabilities in relativistic nuclear collisions
• Approach to equilibrium in weakly coupled nonabelian plasmas
• Color filamentation in ultrarelativistic heavy-ion collisions
• The Boltzmann equation for gluons at early times after a heavy ion collision
• Initial conditions for hydrodynamics from weakly coupled pre-equilibrium evolution
• The Abelianization of QCD Plasma Instabilities
• Thermal and Chemical Equilibration in Relativistic Heavy Ion Collisions
• Chemical Equilibration in Hadronic Collisions
• Gluon Transport Equation in the Small Angle Approximation and the Onset of Bose-Einstein Condensation
• Chemical Equilibration in Weakly Coupled QCD
• Quark production, Bose-Einstein condensates and thermalization of the quark-gluon plasma
• Free-streaming approximation in early dynamics of relativistic heavy-ion collisions
• A fully relativistic lattice Boltzmann algorithm
• A microscopic description for polarization in particle scatterings
• The quark-gluon plasma at RHIC
• Solving the Boltzmann Equation on GPU
• Nonequilibrium fixed points in longitudinally expanding scalar theories: infrared cascade, Bose condensation and a challenge for kinetic theory
• Gluon multiplication in high energy heavy ion collisions
• A Possible Modified "bottom-up" Thermalization in Heavy Ion Collisions
• A Framework for Lattice QCD Calculations on GPUs
• Equation of state and collision rate tests of parton cascade models
• Massively parallel simulations of relativistic fluid dynamics on graphics processing units with CUDA
• Relativistic Boltzmann transport approach with Bose-Einstein statistics and the onset of gluon condensation
• Evolution to the Quark-Gluon Plasma
• ZMCintegral: a Package for Multi-Dimensional Monte Carlo Integration on Multi-GPUs
• The thermalization of soft modes in non-expanding isotropic quark gluon plasmas
• Glasma Evolution and Bose-Einstein Condensation with Elastic and Inelastic Collisions
• Boost invariant formulation of the chiral kinetic theory
• Indications of early thermalization in relativistic heavy-ion collisions
• On the relativistic Lattice Boltzmann method for quark-gluon plasma simulations
• Properties of the Boltzmann equation in the classical approximation
• Shear and Bulk Viscosities of a Weakly Coupled Quark Gluon Plasma with Finite Chemical Potential and Temperature---Leading-Log Results
• Negative Off-Diagonal Conductivities in a Weakly Coupled Quark Gluon Plasma
• Studies of parton thermalization at RHIC
• Kinetic description of Bose-Einstein condensation with test particle simulations
• ZMCintegral-v5: Support for Integrations with the Scanning of Large Parameter Grids on Multi-GPUs
• Gluon Transport Equation with Effective Mass and Dynamical Onset of Bose-Einstein Condensation
• Lattice Boltzmann method for relativistic hydrodynamics: Issues on conservation law of particle number and discontinuities
• Fixed points and flow analysis on off-equilibrium dynamics in the boson Boltzmann equation
• Kinetic approach to a relativistic BEC with inelastic processes
• Hard-loop dynamics of non-abelian plasma instabilities
• Thermal Relaxation Time in Chemically Non-equilibrated Quark- Gluon Plasma
• Early thermalization of quark-gluon matter with the elastic scattering of ggq and ggqbar
• Relativistic fluid dynamics in heavy ion collisions
• Review of the "Bottom-Up" scenario
• Early thermalization of quark-gluon matter initially created in high-energy nucleus-nucleus collisions
• The role of the gluonic gg<->ggg interactions in early thermalization in ultrarelativistic heavy-ion collisions

Cited by in corpus (10)

• Lepton pair photoproduction in peripheral relativistic heavy-ion collisions
• Charge-dependent directed flows in heavy-ion collisions by Boltzmann-Maxwell equations
• Anomalous magnetohydrodynamics with temperature-dependent electric conductivity and application to the global polarization
• Photoproduction of $e^{+}{e}^{-}$ in peripheral isobar collisions
• JefiGPU: Jefimenko's Equations on GPU
• Two typical collective behaviors of the heavy ions expanding in cold plasma with ambient magnetic field
• Recent developments in chiral and spin polarization effects in heavy-ion collisions
• Nuclear deformation effects in photoproduction of $\rho$ mesons in ultraperipheral isobaric collisions
• Lepton pair production in ultra-peripheral collisions
• Quark polarization from parton scatterings in heavy ion collisions