Electrical conductivity and relaxation via colored noise in a hadronic gas

TL;DR

This paper computes electrical conductivity and relaxation times in a hadronic gas using the Green-Kubo formula and realistic simulations, revealing the impact of resonance lifetimes on current relaxation.

Contribution

It introduces a numerical approach employing the SMASH transport code to evaluate electrical properties of hadron gases with realistic interactions and resonance effects.

Findings

Electrical conductivity values between T=60 MeV and T=150 MeV.

Resonance lifetimes do not significantly affect electric current relaxation.

Comparison with other models validates the approach.

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.