Effect of magnetic field on the charge and thermal transport properties of hot and dense QCD matter

Abstract

We have studied the effect of strong magnetic field on the charge and thermal transport properties of hot QCD matter at finite chemical potential. For this purpose, we have calculated the electrical conductivity ($$\sigma _\mathrm{el}$$σel) and the thermal conductivity ($$\kappa $$κ) using kinetic theory in the relaxation time approximation, where the interactions are subsumed through the distribution functions within the quasiparticle model at finite temperature, strong magnetic field and finite chemical potential. This study helps to understand the impacts of strong magnetic field and chemical potential on the local equilibrium by the Knudsen number ($$\Omega $$Ω) through $$\kappa $$κ and on the relative behavior between thermal conductivity and electrical conductivity through the Lorenz number (L) in the Wiedemann–Franz law. We have observed that, both $$\sigma _\mathrm{el}$$σel and $$\kappa $$κ get increased in the presence of strong magnetic field, and the additional presence of chemical potential further increases their magnitudes, where $$\sigma _\mathrm{el}$$σel shows decreasing trend with the temperature, opposite to its increasing behavior in the isotropic medium, whereas $$\kappa $$κ increases slowly with the temperature, contrary to its fast increase in the isotropic medium. The variation in $$\kappa $$κ explains the decrease of the Knudsen number with the increase of the temperature. However, in the presence of strong magnetic field and finite chemical potential, $$\Omega $$Ω gets enhanced and approaches unity, thus, the system may move slightly away from the equilibrium state. The Lorenz number ($$\kappa /(\sigma _\mathrm{el} T))$$κ/(σelT)) in the abovementioned regime of strong magnetic field and finite chemical potential shows linear enhancement with the temperature and has smaller magnitude than the isotropic one, thus, it describes the violation of the Wiedemann–Franz law for the hot and dense QCD matter in the presence of a strong magnetic field.

Viscous properties of hot and dense QCD matter in the presence of a magnetic field

“…So, the properties of transport coefficients might be robustly influenced by the emergence of strong magnetic field and finite chemical potential. In this process, we have recently studied the charge and thermal transport properties by calculating the electrical conductivity (σ el ) and the thermal conductivity (κ) in the presence of both strong magnetic field and chemical potential and also observed their applications to understand the effects of strong magnetic field and chemical potential on the local equilibrium by the Knudsen number ( ) and on the Lorenz number (L) in the Wiedemann-Franz law [24]. Our aim in this work is to investigate the viscous properties of the hot QCD matter by calculating the shear viscosity (η) and the bulk viscosity (ζ ) in the abovementioned environment of strong magnetic field and finite but small quark chemical potential.…”

“…In order to calculate the Prandtl number for the hot QCD matter in the presence of both strong magnetic field and chemical potential, we require the expressions of shear viscosity, thermal conductivity, mass density and specific heat at constant pressure. We have recently calculated the thermal conductivity in the similar environment [24], so, we have taken the results on κ from our work (appendix A). Then we have determined the mass density from the product of the number densities of quarks, antiquarks and gluons with their respective quasiparticle masses as…”

“…Substituting quark (80) and gluon (81) propagators in Eq. 79, we have calculated the quark self-energy in the imaginary time formalism at strong magnetic field and finite chemical potential, and its approximated form for T > μ f is written [24] as…”

“…Finally, from the Schwinger-Dyson equation 78, the effective mass (squared) of quark in the presence of strong magnetic field, finite temperature and finite chemical potential is obtained (in appendix C) by taking the p 0 = 0, p z → 0 limit [24] as…”

“…where ζ(s) is the Riemann zeta function with s = 3, 5 here. For a thermal medium at finite magnetic field, the quark self-energy is written in the general covariant form [16,100] as Finally, the effective mass (squared) of quark in the presence of strong magnetic field, finite temperature and finite chemical potential is determined by taking the p 0 = 0, p z → 0 limit of either X 2 1 or Y 2 1 (both of them are equal in this limit) [24],…”