Anisotropic electrical conductivity of magnetized hot quark matter

Abstract: We studied the effect of a strong magnetic field ($B$) on the electrical conductivity of hot quark matter. The electrical conductivity is a key transport coefficient determining the time dependence and strength of magnetic fields generated in a relativistic heavy-ion collision. A~magnetic field induces Hall anisotropic conduction, phase-space Landau-level quantization and, if sufficiently strong, interferes with prominent QCD phenomena such as dynamical quark mass generation, likely affecting the quark matter electrical conductivity, which depends strongly on the quark masses. To address these issues, we used a quasi-particle description of quark matter in which the electric charge carriers are constituent quarks with temperature- and magnetic-field-dependent masses predicted by a Nambu--Jona-Lasinio model. The model accurately describes recent lattice QCD results showing magnetic catalysis at low temperatures and inverse magnetic catalysis at temperatures close to the pseudo-critical temperature ($T_{\rm pc}$) of the QCD phase transition. We found that the magnetic field increases the conductivity component parallel to it and decreases the transverse component, in qualitative agreement with recent lattice QCD results. In addition, we found that: (1)~the space anisotropy of the conductivity increases with~$B$, (2)~the longitudinal conductivity increases due to phase-space Landau-level quantization, (3)~a lowest Landau level approximation behaves poorly for temperatures close to $T_{\rm pc}$, and (5)~inverse magnetic catalysis leaves a distinctive signal in all components of the conductivity, a prominent peak at $T_{\rm pc}$. Our study adds to the existing body of work on the hot quark matter electrical conductivity by incorporating nontrivial temperature and magnetic field effects on dynamical mass generation.