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Register a new userCalculation of anisotropic transport coefficients for an ultrarelativistic Boltzmann gas in a magnetic field within a kinetic approach
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According to the Kubo formulas we employ the (3+1)-d parton cascade, Boltzmann approach of multiparton scatterings (BAMPS), to calculate the anisotropic transport coefficients (shear viscosity and electric conductivity) for an ultrarelativistic Boltzmann gas in the presence of a magnetic field. The results are compared with those recently obtained by using the Grads approximation. We find good agreements between both results, which confirms the general use of the derived Kubo formulas for calculating the anisotropic transport coefficients of quark-gluon plasma in a magnetic field.
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The Enskog-Landau kinetic equation is considered to describe non-equilibrium processes of a mixture of charged hard spheres. This equation has been obtained in our previous papers by means of the non-equilibrium statistical operator method. The normal solution of this kinetic equation found in the first approximation using the standard Chapman-Enskog method is given. On the basis of the found solution the flows and transport coefficients have been calculated. All transport coefficients for multicomponent mixture of spherical Coulomb particles are presented analytically for the first time. Numerical calculations of thermal conductivity and thermal diffusion coefficient are performed for some specific mixtures of noble gases of high density. We compare the calculations with those ones for point-like neutral and charged particles.
The transport coefficients of causal relativistic dissipative fluid dynamics are calculated both in a field-theoretical and a kinetic approach. We find that the results from the traditional kinetic calculation by Israel and Stewart are modified. The new expressions for the viscous transport coefficients agree with the results obtained in the field-theoretical approach when the contributions from pair creation and annihilation are neglected.
We compute the shear and bulk viscosities, as well as the thermal conductivity of an ultrarelativistic fluid obeying the relativistic Boltzmann equation in 2+1 space-time dimensions. The relativistic Boltzmann equation is taken in the single relaxation time approximation, based on two approaches, the first, due to Marle and using the Eckart decomposition, and the second, proposed by Anderson and Witting and using the Landau-Lifshitz decomposition. In both cases, the local equilibrium is given by a Maxwell-Juettner distribution. It is shown that, apart from slightly different numerical prefactors, the two models lead to a different dependence of the transport coefficients on the fluid temperature, quadratic and linear, for the case of Marle and Anderson-Witting, respectively. However, by modifying the Marle model according to the prescriptions given in Ref.[1], it is found that the temperature dependence becomes the same as for the Anderson-Witting model.
An intense transient magnetic field is produced in high energy heavy-ion collisions mostly due to the spectator protons inside the two colliding nucleus. The magnetic field introduces anisotropy in the medium and hence the isotropic scalar transport coefficients become anisotropic and split into multiple components. Here we calculate the anisotropic transport coefficients shear, bulk viscosity, electrical conductivity, and the thermal diffusion coefficients for a multicomponent Hadron- Resonance-Gas (HRG) model for a non-zero magnetic field by using the Boltzmann transport equation in a relaxation time approximation (RTA). The anisotropic transport coefficient component along the magnetic field remains unaffected by the magnetic field, while perpendicular dissipation is governed by the interplay of the collisional relaxation time and the magnetic time scale, which is inverse of the cyclotron frequency. We calculate the anisotropic transport coefficients as a function of temperature and magnetic field using the HRG model. The neutral hadrons are unaffected by the Lorentz force and do not contribute to the anisotropic transports, we estimate within the HRG model the relative contribution of isotropic and anisotropic transports as a function of magnetic field and temperature. We also give an estimation of these anisotropic transport coefficients for the hadronic gas at finite baryon chemical potential.
Motivated by a recent finding of an exact solution of the relativistic Boltzmann equation in a Friedmann-Robertson-Walker spacetime, we implement this metric into the newly developed transport approach Simulating Many Accelerated Strongly-interacting Hadrons (SMASH). We study the numerical solution of the transport equation and compare it to this exact solution for massless particles. We also compare a different initial condition, for which the transport equation can be independently solved numerically. Very nice agreement is observed in both cases. Having passed these checks for the SMASH code, we study a gas of massive particles within the same spacetime, where the particle decoupling is forced by the Hubble expansion. In this simple scenario we present an analysis of the freeze-out times, as function of the masses and cross sections of the particles. The results might be of interest for their potential application to relativistic heavy-ion collisions, for the characterization of the freeze-out process in terms of hadron properties.
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