One particle distribution function and shear viscosity in magnetic field: a relaxation time approach

Abstract

We calculate the $\delta f$ correction to the one particle distribution function in presence of magnetic field and non-zero shear viscosity within the relaxation time approximation. The $\delta f$ correction is found to be electric charge dependent. Subsequently, we also calculate one longitudinal and four transverse shear viscous coefficients as a function of dimensionless Hall parameter ${\chi }_H$ in presence of the magnetic field. We find that a proper linear combination of the shear viscous coefficients calculated in this work scales with the result obtained from Grad's moment method in \cite{Denicol:2018rbw}. Calculation of invariant yield of ${\pi }^{-}$ in a simple Bjorken expansion with cylindrical symmetry shows no noticeable change in spectra due to the $\delta f$ correction for realistic values of the magnetic field and relaxation time. However, when transverse expansion is taken into account using a blast wave type flow field we found noticeable change in spectra and elliptic flow coefficients due to the $\delta f$ correction. The $\delta f$ is also found to be very sensitive on the magnitude of magnetic field. Hence we think it is important to take into account the $\delta f$ correction in more realistic numerical magnetohydrodynamics simulations.

arXiv comment14 pages, 6 figures, revised version, new section added, new figures added, published in EPJA

References in corpus (38)

• The effects of topological charge change in heavy ion collisions: "Event by event P and CP violation"
• Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC?
• Conformal Relativistic Viscous Hydrodynamics: Applications to RHIC results at sqrt(s_NN) = 200 GeV
• Event-by-event generation of electromagnetic fields in heavy-ion collisions
• The Effect of Shear Viscosity on Spectra, Elliptic Flow, and HBT Radii
• Event-by-event fluctuations of magnetic and electric fields in heavy ion collisions
• Suppression of elliptic flow in a minimally viscous quark-gluon plasma
• Magnetohydrodynamics, charged currents and directed flow in heavy ion collisions
• Higher flow harmonics from (3+1)D event-by-event viscous hydrodynamics
• Multiplicity scaling in ideal and viscous hydrodynamics
• Time and space dependence of electromagnetic field in relativistic heavy-ion collisions
• Numerical magneto-hydrodynamics for relativistic nuclear collisions
• Influence of a temperature-dependent shear viscosity on the azimuthal asymmetries of transverse momentum spectra in ultrarelativistic heavy-ion collisions
• Conformal anomaly as a source of soft photons in heavy ion collisions
• Particle spectra in Pb-Pb collisions at 2.76 TeV
• Anisotropic Hydrodynamics, Bulk Viscosities and R-Modes of Strange Quark Stars with Strong Magnetic Fields
• Synchrotron radiation by fast fermions in heavy-ion collisions
• Analytic Bjorken flow in one-dimensional relativistic magnetohydrodynamics
• Kubo formulas for relativistic fluids in strong magnetic fields
• Bjorken flow in one-dimensional relativistic magnetohydrodynamics with magnetization
• Electromagnetic fields with electric and chiral magnetic conductivities in heavy ion collisions
• Electromagnetic field and the chiral magnetic effect in the quark-gluon plasma
• Photon decay in strong magnetic field in heavy-ion collisions
• The viscosity of quark-gluon plasma at RHIC and the LHC
• Bulk Viscosity of Quark-Gluon Plasma in Strong Magnetic Fields
• Electromagnetic response of quark-gluon plasma in heavy-ion collisions
• Effect of intense magnetic fields on reduced-MHD evolution in $\sqrt{s_{\mathrm{NN}}}$ = 200 GeV Au+Au collisions
• Event-by-event distribution of magnetic field energy over initial fluid energy density in $\sqrt{s_{\mathrm{NN}}}$= 200 GeV Au-Au collisions
• Shear Viscosity of Quark-Gluon Plasma in Weak Magnetic Field in Perturbative QCD: Leading Log
• The QGP shear viscosity -- elusive goal or just around the corner?
• Transverse flow induced by inhomogeneous magnetic fields in the Bjorken expansion
• Magnetic field-induced squeezing effect at RHIC and at the LHC
• Comparison of results from a 2+1D relativistic viscous hydrodynamic model to elliptic and hexadecapole flow of charged hadrons measured in Au-Au collisions at $\sqrt{s_{\mathrm{NN}}}$ = 200 GeV
• Wigner functions of massive fermions in strong magnetic fields
• Femtoscopic signature of strong radial flow in high-multiplicity $pp$ collisions
• Shear viscosity in magnetized neutron star crust
• The Shear Viscosity in an Anisotropic Unitary Fermi Gas
• Non-relativistic approximate numerical ideal-magneto hydrodynamics of (1+1) D transverse flow in Bjorken scenario

Cited by in corpus (28)

• Relativistic Spin Magnetohydrodynamics
• Anisotropic transport properties of Hadron Resonance Gas in magnetic field
• New developments in relativistic magnetohydrodynamics
• Transport coefficients of hot and dense hadron gas in a magnetic field: a relaxation time approach
• Anisotropic electrical conductivity of magnetized hot quark matter
• Relativistic non-resistive viscous magnetohydrodynamics from the kinetic theory:a relaxation time approach
• New Developments in Relativistic Fluid Dynamics with spin
• Extended relaxation time approximation and relativistic dissipative hydrodynamics
• Heavy quark dynamics in a hot magnetized QCD medium
• Electrical conductivity of a hot and dense QGP medium in a magnetic field
• Impact of magnetic field on shear viscosity of quark matter in Nambu-Jona-Lasinio model
• Kubo estimation of the electrical conductivity for a hot relativistic fluid in the presence of a magnetic field
• Quantum expression for the electrical conductivity of massless quark matter and of the hadron resonance gas in the presence of a magnetic field
• One-loop Kubo estimations of the shear and bulk viscous coefficients for hot and magnetized Bosonic and Fermionic systems
• Calculation of anisotropic transport coefficients for an ultrarelativistic Boltzmann gas in a magnetic field within a kinetic approach
• Longitudinal conductivity of hot magnetized collisional QCD medium in the inhomogeneous electric field
• Effect of time-varying electromagnetic field on Wiedemann-Franz law in a hot hadronic matter
• Thermal transport in a weakly magnetized hot QCD medium
• Relativistic second-order viscous hydrodynamics from kinetic theory with extended relaxation-time approximation
• Relaxation time approximation with pair production and annihilation processes
• Quantum version of transport coefficients in Nambu--Jona-Lasinio model at finite temperature and strong magnetic field
• Effect of Coriolis force on the shear viscosity of quark matter: A nonrelativistic description
• Shear viscosity coefficient of magnetized QCD medium near chiral phase transition
• Transport Coefficients of relativistic matter: A detailed formalism with a gross knowledge of their magnitude
• Effect of magnetic field on jet transport coefficient $\hat{q}$
• Non-relativistic transport from frame-indifferent kinetic theory
• Order-by-order Anisotropic Transport Coefficients of a Magnetised Fluid: a Chapman-Enskog Approach
• Physics of strong electromagnetic fields in relativistic heavy-ion collisions