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.

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Heavy quark observables are applied to probe the initial energy density distribution with violation of longitudinal boost invariance produced in relativistic heavy-ion collisions. Using an improved Langevin model coupled to a (3+1)-dimensional viscous hydrodynamic model, we study the nuclear modification factor (RAA), directed flow (v1) and elliptic flow (v2) coefficients of heavy mesons and their decayed electrons at the RHIC energy. We find that the counter-clockwise tilt of the nuclear matter in the reaction plane results in a positive (negative) heavy flavor v1 in the backward (forward) rapidity region, whose magnitude increases with the heavy quark transverse momentum. The difference in the heavy flavor RAA between different angular regions is also proposed as a complementary tool to characterize the asymmetry of the medium profile. Our model results are consistent with currently available data at RHIC and provide predictions that can be tested by future measurements.