Thermoelectric properties of the (an-)isotropic QGP in magnetic fields
He-Xia Zhang, Jin-Wen Kang, Ben-Wei Zhang
Abstract
Abstract The Seebeck effect and the Nernst effect, which reflect the appearance of electric fields along x -axis and along y -axis ( $$E_{x}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>E</mml:mi> <mml:mi>x</mml:mi> </mml:msub> </mml:math> and $$E_{y}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>E</mml:mi> <mml:mi>y</mml:mi> </mml:msub> </mml:math> ), 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 ( $$S_{xx}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>S</mml:mi> <mml:mrow> <mml:mi>xx</mml:mi> </mml:mrow> </mml:msub> </mml:math> ) 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 ( $$\mu _{q}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>μ</mml:mi> <mml:mi>q</mml:mi> </mml:msub> </mml:math> ) on these thermoelectric transport coefficients are investigated. In the presence (absence) of weak magnetic field, we find $$S_{xx}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>S</mml:mi> <mml:mrow> <mml:mi>xx</mml:mi> </mml:mrow> </mml:msub> </mml:math> for a fixed $$\mu _{q}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>μ</mml:mi> <mml:mi>q</mml:mi> </mml:msub> </mml:math> 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 $$S_{xx}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>S</mml:mi> <mml:mrow> <mml:mi>xx</mml:mi> </mml:mrow> </mml:msub> </mml:math> decreases with increasing temperature. Unlike $$S_{xx}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>S</mml:mi> <mml:mrow> <mml:mi>xx</mml:mi> </mml:mrow> </mml:msub> </mml:math> , 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 ( $$S_{zz}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>S</mml:mi> <mml:mrow> <mml:mi>zz</mml:mi> </mml:mrow> </mml:msub> </mml:math> ) exists. Our results show that the value of $$S_{zz}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>S</mml:mi> <mml:mrow> <mml:mi>zz</mml:mi> </mml:mrow> </mml:msub> </mml:math> at a fixed $$\mu _{q}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>μ</mml:mi> <mml:mi>q</mml:mi> </mml:msub> </mml:math> in the lowest Landau level (LLL) approximation always remains positive. Within the effect of high Landau levels, $$S_{zz}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>S</mml:mi> <mml:mrow> <mml:mi>zz</mml:mi> </mml:mrow> </mml:msub> </mml:math> exhibits a thermal structure similar to that in the LLL approximation. As the Landau level increases further, $$S_{zz}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>S</mml:mi> <mml:mrow> <mml:mi>zz</mml:mi> </mml:mrow> </mml:msub> </mml:math> 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.