Revisit to electrical and thermal conductivities, Lorenz and Knudsen numbers in thermal QCD in a strong magnetic field

We have explored how the electrical (sigma(el)) and thermal (kappa) conductivities in a thermal QCD medium get affected in weak-momentum anisotropies arising either due to a strong magnetic field or due to asymptotic expansion in a particular direction. This study, in turn, facilitates to understand the longevity of strong magnetic field through sigma(el), Lorenz number in Wiedemann-Franz law, and the validity of local equilibrium by the Knudsen number through kappa. We calculate the conductivities by solving the relativistic Boltzmann transport equation in relaxation-time approximation, where the interactions are incorporated through the distribution function within the quasiparticle approach at finite T and strong B. However, we also compare with the noninteracting scenario, which gives unusually large values, thus validating the quasiparticle description. We have found that both sigma(el) and kappa get enhanced in a magnetic field-driven anisotropy, but sigma(el) monotonically decreases with the temperature, opposite to the faster increase in the expansion-driven anisotropy. Whereas kappa increases very slowly with the temperature, contrary to its rapid increase in the expansion-driven anisotropy. Therefore, the conductivities may distinguish the origin of anisotropies. The above findings are broadly attributed to three factors: the stretching and squeezing of the distribution function due to the momentum anisotropies generated by the strong magnetic field and asymptotic expansion, respectively, the dispersion relation and the resulting phase-space factor, the relaxation-time in the absence and presence of strong magnetic field. Thus, sigma(el) extracts the time-dependence of initially produced strong magnetic field, which expectedly decays slower than in vacuum but the expansion-driven anisotropy makes the decay faster. The variation in kappa transpires that the Knudsen number (Omega) decreases with the temperature, but the expansion-driven anisotropy reduces its magnitude, and the strong magnetic field-driven anisotropy raises its value but to less than one, thus the system can still be in local equilibrium in a range of temperature and magnetic field. Finally, the ratio, kappa/sigma(el) in Wiedemann-Franz law in magnetic field-driven anisotropy increases linearly with temperature but its magnitude is smaller than in expansion-driven anisotropic medium. Thus, the slope, i.e., the Lorenz number can make the distinction between the anisotropies of different origins.