Abstract
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.
Highlights
In high-energy collisions of heavy nuclei, such as those at the Large Hadron Collider (LHC) or the Relativistic Heavy-Ion Collider (RHIC) facilities, a transient state of hot deconfined matter is created
In this work we address the hydrodynamic fluctuations and the computation of the electrical conductivity by addressing the dynamics of individual particles simulated in a transport model
In the right panel we show the value of the relaxation time of the electric current as a function of the temperature
Summary
In high-energy collisions of heavy nuclei, such as those at the Large Hadron Collider (LHC) or the Relativistic Heavy-Ion Collider (RHIC) facilities, a transient state of hot deconfined matter is created. Their dynamics depends by Maxwell’s equations on the electrical conductivity This coefficient was computed in hadronic kinetic theory [27], partonic transport models [39,40], off-shell transport and dynamical quasiparticle models [41,42,43,44], holography [45,46,47], lattice QCD [29,48,49,50], DysonSchwinger calculations [51], in the Polyakov-extended quark-meson model [52], semianalytic calculations within perturbative QCD [53,54,55], and taking into account strong magnetic fields [56,57].
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