Thermoelectric properties of the (an-)isotropic QGP in magnetic fields

He-Xia Zhang; Jin-Wen Kang; Ben-Wei Zhang

doi:10.1140/epjc/s10052-021-09409-w

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2021) 81: 623
https://doi.org/10.1140/epjc/s10052-021-09409-w

Regular Article - Theoretical Physics

Thermoelectric properties of the (an-)isotropic QGP in magnetic fields

He-Xia Zhang¹, Jin-Wen Kang¹ and Ben-Wei Zhang¹^,2^c

¹ Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, 430079, Wuhan, China
² Institute of Quantum Matter, South China Normal University, 510006, Guangzhou, China

^c bwzhang@mail.ccnu.edu.cn

Received: 24 January 2021
Accepted: 5 July 2021
Published online: 17 July 2021

Abstract

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 ( $μ_{q}$ $\mu _{q}$ ) on these thermoelectric transport coefficients are investigated. In the presence (absence) of weak magnetic field, we find $S_{xx}$ $S_{xx}$ for a fixed $μ_{q}$ $\mu _{q}$ 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 $S_{xx}$ $S_{xx}$ 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 $μ_{q}$ $\mu _{q}$ 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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