Abstract
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.
Highlights
Quantum chromodynamics (QCD) is the fundamental theory of the strong interaction, and the Lattice QCD calculations have predicted a crossover phase transition from the hadronic matter to the quark–gluon plasma (QGP) can be realized with the increase of temperature at the small or vanishing baryon chemical potential [1,2]
The associated Seebeck and Nernst signal are the functions regarding the electrical conductivity tensors and the thermoelectric conductivity tensors, which can be obtained by solving the relativistic Boltzmann equation under the relaxation time approximation
We found in the presence of weak magnetic field along z-axis, Sxx for a nonzero quark chemical potential is negative in sign, indicating that the dominant charge carriers for converting heat gradient into electric field are negatively charged quarks
Summary
Quantum chromodynamics (QCD) is the fundamental theory of the strong interaction, and the Lattice QCD calculations have predicted a crossover phase transition from the hadronic matter to the quark–gluon plasma (QGP) can be realized with the increase of temperature at the small or vanishing baryon chemical potential [1,2]. 2, we derive the general formulas of thermoelectric and electric conductivity tensors in an (an-)isotropic medium at the weak magnetic field by solving the relativistic Boltzmann equation under the relaxation time approximation (RTA). Using the Onsager reciprocity relation of the thermoelectric and electric conductivity tensors in a magnetic field, σxx,a(αxx,a) = σyy,a(αyy,a) and σxy,a(αxy,a) = −σyx,a(−αyx,a), we derive the expressions of the Seebeck coefficient (Sxx,a) and the Nernst signal (Na) for ath species from Eqs. Due to the motion of (anti-)quarks in the Landau quantization is mainly restricted to the direction of magnetic field, the equilibrium distribution function of charge particle fB,a in an isotropic medium and in an anisotropic medium induced by strong magnetic field can read as fB,a( pz, μa) fB0,a fBξ ,a e(. With αzz (σzz) being the total longitudinal thermoelectric (electrical) conductivity
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