Abstract
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. The in-medium cross sections vis-\`a-vis the relaxation time for $\ensuremath{\pi}\ensuremath{\pi}$ scattering are obtained using a one-loop modified thermal propagator for the exchanged $\ensuremath{\rho}$ and $\ensuremath{\sigma}$ 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 the 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 the vacuum cross section is used.
Highlights
The study of strongly interacting matter in the presence of a background magnetic field has significant applications in many physical systems
As it was previously mentioned, the produced magnetic field persists for a longer time if the value of electrical conductivity of the medium is large, which is a possibility for the case of quark-gluon plasma (QGP)
We have evaluated the conductivity tensor using the Boltzmann transport equation in a magnetic field and evaluated the electrical conductivity, Hall conductivity, and σ2 for a system consisting of a pion gas
Summary
The study of strongly interacting matter in the presence of a background magnetic field has significant applications in many physical systems (see Ref. [1] for a review). It is observed that the transverse electrical conductivity is dominated by the Hall conductivity, and the parallel conductivity has a nominal dependence on both T and μ As it was previously mentioned, the produced magnetic field persists for a longer time if the value of electrical conductivity of the medium is large, which is a possibility for the case of QGP. We have chosen to calculate the electrical conductivity of pions as they are the most abundant species among the other hadrons produced in the HICs at the RHIC and LHC [50] This type of study is important, as the magnetic field produced in heavy ion collisions is of hadronic scale, and the evaluation of transport coefficients of the QGP and the hadronic medium will provide better insight into the time evolution of strongly interacting matter in the presence of a background magnetic field.
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