Electric Conductivity from the solution of the Relativistic Boltzmann Equation

Abstract

We present numerical results of electric conductivity ${\sigma }_{el}$ of a fluid obtained solving the Relativistic Transport Boltzmann equation in a box with periodic boundary conditions. We compute ${\sigma }_{el}$ using two methods: the definition itself, i.e. applying an external electric field, and the evaluation of the Green-Kubo relation based on the time evolution of the current-current correlator. We find a very good agreement between the two methods. We also compare numerical results with analytic formulas in Relaxation Time Approximation (RTA) where the relaxation time for ${\sigma }_{el}$ is determined by the transport cross section ${\sigma }_{tr}$, i.e. the differential cross section weighted with the collisional momentum transfer. We investigate the electric conductivity dependence on the microscopic details of the 2-body scatterings: isotropic and anisotropic cross-section, and massless and massive particles. We find that the RTA underestimates considerably ${\sigma }_{el}$; for example at screening masses $m_D\sim T$ such underestimation can be as large as a factor of 2. Furthermore, we study a more realistic case for a quark-gluon system (QGP) considering both a quasi-particle model, tuned to lQCD thermodynamics, as well as the case of a pQCD gas with running coupling. Also for these cases more directly related to the description of the QGP system, we find that RTA significantly underestimate the ${\sigma }_{el}$ by about a $60-80\%$.

9 pages, 9 figures

References in corpus (17)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• The Chiral Magnetic Effect
• The order of the quantum chromodynamics transition predicted by the standard model of particle physics
• Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC?
• Universal Quantum Viscosity in a Unitary Fermi Gas
• Spectral functions at small energies and the electrical conductivity in hot, quenched lattice QCD
• Quasi-Particle Theory of Shear and Bulk Viscosities of Hadronic Matter
• Influence of the shear viscosity of the quark-gluon plasma on elliptic flow in ultrarelativistic heavy-ion collisions
• Magnetic-Field-Induced insulator-conductor transition in SU(2) quenched lattice gauge theory
• Perturbative QCD Calculations of Elliptic Flow and Shear Viscosity in Au+Au Collisions at $\sqrt{s_{NN}}=200$ GeV
• Bulk viscosity in quasi particle models
• Hadron spectra and elliptic flow for 200 A GeV Au+Au collisions from viscous hydrodynamics coupled to a Boltzmann cascade
• Scalings of Elliptic Flow for a Fluid at Finite Shear Viscosity
• NNLO hard-thermal-loop thermodynamics for QCD
• Elliptic flow of gluon matter in ultrarelativistic heavy-ion collisions
• Investigation of Heat Conductivity in Relativistic Systems using a Partonic Cascade
• Shear Viscosity in a Perturbative Quark-Gluon-Plasma

Cited by in corpus (3)

• Electrical conductivity and Hall conductivity of hot and dense hadron gas in a magnetic field: a relaxation time approach
• Electrical Conductivity of an Anisotropic Quark Gluon Plasma : A Quasiparticle Approach
• Electrical conductivity of hadronic matter from different possible mesonic and baryonic thermal fluctuations