Thermoelectric properties of the (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.