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 quasiparticle 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 pseudocritical temperature ($T_{\mathrm{pc}}$) 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 $T_{\mathrm{pc}}$, and (5) inverse magnetic catalysis leaves a distinctive signal in all components of the conductivity, a prominent peak at $T_{\mathrm{pc}}$. 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. Our results are useful both for studies employing magnetohydrodynamics simulations of heavy-ion collisions and for getting insight on lattice QCD results.

We have calculated the temperature dependence of shear $\eta$ and bulk $\zeta$ viscosities of quark matter due to quark-meson fluctuations. The quark thermal width originating from quantum fluctuations of quark-$\pi$ and quark-$\sigma$ loops at finite temperature is calculated with the formalism of real-time thermal field theory. Temperature-dependent constituent-quark and meson masses and quark-meson couplings are obtained in the Nambu–Jona-Lasinio model. We found a nontrivial influence of the temperature-dependent masses and couplings on the Landau-cut structure of the quark self-energy. Our results for the ratios $\eta /s$ and $\zeta /s$, where $s$ is the entropy density (also determined in the Nambu–Jona-Lasinio model in the quasiparticle approximation), are in fair agreement with results of the literature obtained from different models and techniques. In particular, our result for $\eta /s$ has a minimum very close to the quantum lower bound, $\eta /s=1/4\pi$.

We have calculated the shear viscosity coefficient $$\eta${}$ of the strongly interacting matter in the relaxation time approximation, where a quasiparticle description of quarks with their dynamical masses is considered from the Nambu-Jona-Lasinio model. Due to the thermodynamic scattering of quarks with pseudoscalar-type condensate (i.e., pion), a nonzero Landau damping will be acquired by the propagating quarks. This Landau damping may be obtained from the Landau cut contribution of the in-medium self-energy of a quark-pion loop, which is evaluated in the framework of real-time thermal field theory.

We have investigated the shear viscosity of quark matter in the presence of a strong uniform magnetic field background in which the Nambu-Jona-Lasinio model has been considered to describe the magnetothermodynamical properties of the medium. In the presence of magnetic field, the shear viscosity coefficient gets split into different components because of anisotropy in tangential stress of the fluid. Four different components can be merged to two components in the strong field limit, at which the collisional width of the quark becomes much lower than its synchrotron frequency. A simplified contact diagram of quark-quark interaction can estimate a small collisional width, for which the strong field limit expressions are exactly applicable, although for the Relativistic Heavy Ion Collider or LHC matter, one can expect a large thermal width, for which generalized four-component viscosities are necessary. We have explored all these different possible cases in the thermodynamical framework of the Nambu--Jona-Lasinio model.