Studying the thermoelectric properties of an anisotropic QGP medium

TL;DR

The paper investigates how expansion-induced momentum anisotropy, quantified by $\xi$, affects the thermoelectric response of the QGP produced in ultrarelativistic heavy-ion collisions. Using a relativistic Boltzmann transport equation in the relaxation-time approximation within a quasiparticle model, it computes the flavor-resolved Seebeck coefficients $S_f$ and the total Seebeck coefficient $S$ under a temperature gradient with vanishing current. The main finding is that anisotropy enhances the Seebeck coefficient, with a more pronounced effect on the total $S$ due to increased parton densities and modified masses, while $S$ generally decreases with temperature and increases with chemical potential. These results suggest stronger thermoelectric currents and potential observable signatures, such as charge asymmetries and modified electromagnetic spectra, in the early, anisotropic stages of QGP evolution.

Abstract

We have studied how the thermoelectric properties of the quark-gluon plasma (QGP) are affected by a weak-momentum anisotropy arising from the asymptotic expansion of matter in the initial stages of ultrarelativistic heavy-ion collisions. The highly energetic medium produced in such collisions exhibits a notable temperature difference between its central and peripheral regions. This temperature gradient induces an electric field whose magnitude per unit temperature gradient, in the limit of vanishing electric current, defines the Seebeck coefficient of the medium. We have calculated the Seebeck coefficient for both individual quark flavors and the entire QGP medium in the presence of expansion-induced anisotropy by solving the relativistic Boltzmann transport equation in the relaxation time approximation within the kinetic theory framework. The partonic interactions are incorporated through their effective thermal masses within the quasiparticle model for an anisotropic QGP medium. We have observed that the magnitude of the Seebeck coefficient for each quark flavor as well as for the entire QGP medium increases in the presence of expansion-induced anisotropy, indicating a stronger induced electric field in the anisotropic medium compared to the isotropic case. Given that an increase in the Seebeck coefficient may lead to observable signatures such as charge asymmetries in particle distributions and to modifications in the transport behavior of the QGP, these results may provide useful input for future phenomenological studies investigating the internal structure and phase properties of the QGP in heavy-ion collisions.

Figures (7)

• Figure 1: Variation of the quasiparticle mass of quark, normalized to its value in an isotropic medium, as a function of temperature for (a) $\xi=0.2$ and (b) $\xi=0.6$.
• Figure 2: Temperature dependence of the (a) $u$ quark and (b) $d$ quark distribution functions, normalized to their isotropic counterparts, for different values of the anisotropy parameter.
• Figure 3: (a) Temperature dependence of the $s$ quark distribution function and (b) momentum dependence of the $u$ quark distribution function, both normalized to their isotropic counterparts, for different values of the anisotropy parameter.
• Figure 4: Momentum dependence of the (a) $d$ quark and (b) $s$ quark distribution functions, normalized to their isotropic counterparts, for different values of the anisotropy parameter.
• Figure 5: Variation of Seebeck coefficient as a function of temperature for (a) $u$ quark and (b) $d$ quark.