The Seebeck effect and the Nernst effect, which reflect the appearance of electric fields along x-axis and along y-axis ($$E_{x}$$ E x and $$E_{y}$$ 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 ($$S_{xx}$$ 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 ($$\mu _{q}$$ μ q ) on these thermoelectric transport coefficients are investigated. In the presence (absence) of weak magnetic field, we find $$S_{xx}$$ S xx for a fixed $$\mu _{q}$$ μ 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 $$S_{xx}$$ S xx decreases with increasing temperature. Unlike $$S_{xx}$$ 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 ($$S_{zz}$$ S zz ) exists. Our results show that the value of $$S_{zz}$$ S zz at a fixed $$\mu _{q}$$ μ q in the lowest Landau level (LLL) approximation always remains positive. Within the effect of high Landau levels, $$S_{zz}$$ S zz exhibits a thermal structure similar to that in the LLL approximation. As the Landau level increases further, $$S_{zz}$$ 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.

We investigate the chiral phase structure of quark matter with spheroidal momentum-space anisotropy specified by one anisotropy parameter in the 2+1 flavor quark-meson model. We find that the chiral phase diagram and the location of the critical endpoint (CEP) are significantly affected by the value of . With an increase in , the CEP is shifted to lower temperatures and higher quark chemical potentials. In addition, the temperature of the CEP is more sensitive to the anisotropy parameter than the corresponding quark chemical potential, which is the opposite to that from the finite system volume effect. The effects of the momentum anisotropy on the thermodynamic properties and scalar (pseudoscalar) meson masses are also studied at the vanishing quark chemical potential. The numerical results reveal that an increase in can hinder the restoration of chiral symmetry. We also find that shear viscosity and electrical conductivity decrease as increases. However, the bulk viscosity exhibits a significant non-trivial behavior with in the entire temperature domain of interest.

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The chiral phase structure, mesonic properties and transport properties in a momentum anisotropic quark matter induced by the preferential expansion of medium are phenomenologically investigated based on the two flavor Nambu-Jona-Lasinio model. The calculations of various transport coefficients have been performed using the kinetic theory in the relaxation time approximation, where the momentum anisotropy is embeded in the estimation of both distribution function and the relaxation time. Our results indicate that an increase in anisotropy parameter ξ can considerably lead to a catalysis of chiral symmetry breaking. The critical endpoint (CEP) is shifted to smaller temperatures and larger quark chemical potentials as ξ increases, and the influence of momentum anisotropy on temperature of CEP is almost the same as that on the quark chemical potential of CEP. The meson masses and the associated decay widths also significantly are affect by the variation of ξ. The temperature behavior of scaled shear viscosity η/T 3 and scaled electrical conductivity σ el /T exhibit a similar dip struture, however, their qualitative behaviors with ξ are different. Nevertheless, the minima of both η/T 3 and σ el /T shift toward higher temperatures with an increase of ξ. Furthermore, in this work the Seebeck coefficient S exhibits a decreasing function of temperature and its sign is positive, indicating the dominant carriers of converting the temperature gradient to the electric field are up quarks. With a rise in ξ the value of S has a significant enhancement for the temperature below the critical temperature.