Thermoelectric properties of (an-)isotropic QGP in magnetic fields

The Seebeck effect and the Nernst effect, which reflect the appearance of electric fields along $x$-axis and along $y$-axis ($E_{x}$ and $E_{y}$), respectively, induced by the thermal gradient along $x$-axis, are studied in the QGP at an external magnetic field along $z$-axis. We calculate the associated Seebeck coefficient ($S_{xx}$) and Nernst signal ($N$) using the relativistic Boltzmann equation under the relaxation time approximation. In an isotropic QGP, the influences of magnetic field ($B$) and quark chemical potential ($\mu_{q}$) on these thermoelectric transport coefficients are investigated. In the presence (absence) of weak magnetic field, we find $S_{xx}$ for a fixed $\mu_{q}$ is negative (positive) in sign, indicating that the dominant carriers for converting heat gradient to electric field are negatively (positively) charged quarks. The absolute value of $S_{xx}$ decreases with increasing temperature. Unlike $S_{xx}$, the sign of $N$ is independent of charge carrier type, and its thermal behavior displays a peak structure. In the presence of strong magnetic field, due to the Landau quantization of transverse motion of (anti-)quarks perpendicular to magnetic field, only the longitudinal Seebeck coefficient ($S_{zz}$) exists. Our results show that the value of $S_{zz}$ at a fixed $\mu_{q}$ in the lowest Landau level (LLL) approximation always remains positive. Within the effect of high Landau levels, $S_{zz}$ exhibits a thermal structure similar to that in the LLL approximation. As the Landau level increases further, $S_{zz}$ decreases and even its sign changes from positive to negative. The computations of these thermoelectric transport coefficients are also extended to a medium with momentum-anisotropy induced by initial spatial expansion as well as strong magnetic field.