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Register a new userElectrical conductivity and relaxation via colored noise in a hadronic gas
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Motivated by the theory of relativistic hydrodynamic fluctuations we make use of the Green-Kubo formula to compute the electrical conductivity and the (second-order) relaxation time of the electric current of an interacting hadron gas. We use the recently developed transport code SMASH to numerically solve the coupled set of Boltzmann equations implementing realistic hadronic interactions. In particular, we explore the role of the resonance lifetimes in the determination of the electrical relaxation time. As opposed to a previous calculation of the shear viscosity we observe that the presence of resonances with lifetimes of the order of the mean-free time does not appreciably affect the relaxation of the electric current fluctuations. We compare our results to other approaches describing similar systems, and provide the value of the electrical conductivity and the relaxation time for a hadron gas at temperatures between T=60 MeV and T=150 MeV.
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We have explored the shear viscosity and electrical conductivity calculations for bosonic and fermionic medium, which goes from without to with magnetic field picture and then their simplified massless expressions. In presence of magnetic field, 5 independent velocity gradient tensors can be designed, so their corresponding proportional coefficients, connected with the viscous stress tensor provide us 5 shear viscosity coefficients. In existing litterateurs, two sets of tensors are available. Starting from them, present work has obtained two sets of expressions for 5 shear viscosity coefficients, which can be ultimately classified into three basic components: parallel, perpendicular and Hall components as one get same for electrical conductivity at finite magnetic field. Our calculations are based on kinetic theory approach in relaxation time approximation. Repeating same mathematical steps for finite magnetic field picture, which traditionally practiced for without field case, we have obtained 2 sets of 5 shear viscosity components, whose final expressions are in well agreements with earlier references, although a difference in methodology or steps can be clearly noticed. Realizing the massless results of viscosity and conductivity for Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein distribution function, we have applied them for massless quark gluon plasma and hadronic matter phases, which can provide us a rough order of strength, within which actual results will vary during quark-hadron phase transition. Present work also indicates that magnetic field might have some role for building perfect fluid nature in RHIC or LHC matter. The lower bound expectation of shear viscosity to entropy density ratio is also discussed.
Effect of quantum chromodynamics (QCD) interaction in quark-gluon plasma on electrical conductivity is studied, where lattice quantum chromodynamics (LQCD) results are mapped through quark and gluon degeneracy.
The electrical and Hall conductivities in a uniform magnetic field are evaluated for an interacting pion gas using the kinetic theory approach within the ambit of relaxation time approximation (RTA). The in-medium cross sections vis-a-vis the relaxation time for $pipi$ scattering are obtained using a one-loop modified thermal propagator for the exchanged $rho$ and $sigma$ mesons using thermal field theoretic techniques. For higher values of the magnetic field, a monotonic increase of the electrical conductivity with the temperature is observed. However, for a given temperature the conductivity is found to decrease steadily with magnetic field. The Hall conductivity, at lower values of the magnetic field, is found to decrease with temperature more rapidly than the electrical conductivity, whereas at higher values of the magnetic field, a linear increase is seen. Use of the in-medium scattering cross-section is found to produce a significant effect on the temperature dependence of both electrical and Hall conductivities compared to the case where vacuum cross-section is used.
The relaxation times over which dissipative fluxes restore their steady state values have been evaluated for a pion gas using the 14-moment method. The effect of the medium has been implemented through a temperature dependent pi-pi cross-section in the collision integral which is obtained by including one-loop self-energies in the propagators of the exchanged rho and sigma mesons. To account for chemical freeze out in heavy ion collisions, a temperature dependent pion chemical potential has been introduced in the distribution function. The temperature dependence of the relaxation times for shear and bulk viscous flows as well as the heat flow is significantly affected.
In this work, we study electrical conductivity and Hall conductivity in the presence of electromagnetic field using Relativistic Boltzmann Transport Equation with Relaxation Time Approximation. We evaluate these transport coefficients for a strongly interacting system consisting of nearly massless particles which is similar to Quark-Gluon Plasma and is likely to be formed in heavy-ion collision experiments. We explicitly include the effects of magnetic field in the calculation of relaxation time. The values of magnetic field are obtained for all the centrality classes of Au+Au collisions at $sqrt {s_{rm NN}} =$ 200 GeV and Pb+Pb collisions at $sqrt {s_{rm NN}} =$ 2.76 TeV. We consider the three lightest quark flavors and their corresponding antiparticles in this study. We estimate the temperature dependence of the electrical conductivity and Hall conductivity for different strengths of magnetic field. We observe a significant dependence of temperature on electrical and Hall conductivity in the presence of magnetic field.
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