Thermal and thermoelectric responses of hot QCD medium in time-varying magnetic fields

The thermal response of the hot QCD matter has been studied in the presence of a time-varying magnetic field. The impact of the magnetic field, its time dependence, and the collision aspects of the medium on thermal transport have been studied within the relativistic kinetic theory. The decay time of the magnetic field in the medium seems to have a strong dependence on thermal conductivity. The applicability of the Wiedemann-Franz law for the QCD medium has been investigated in the presence of time-varying external electromagnetic fields. The phenomenological significance of thermal transport in heavy-ion collision experiments has also been investigated by relating the thermal conductivity to the elliptic flow through the Knudsen number. The investigations are extended to study the thermoelectric behavior of hot QCD medium and its dependence on the magnetic field. The time dependent magnetic field is observed to significantly influence the thermoelectric behavior of the medium.

Figure 1

Left: temperature dependence of thermal conductivity ${\kappa }_0$ for two different choices of magnetic field. The result is compared with the transport theory estimation with constant magnetic field [59]. Right: the proper time evolution of ${\kappa }_0$ in the QGP medium. We consider $e{B}_0=0.08{\mathrm{GeV}}^2$ and $\mu =100\mathrm{MeV}$ for the analysis.

Figure 2

Left: the effect of chemical potential and magnetic field decay parameter on ${\kappa }_0$ at a constant temperature $T=200\mathrm{MeV}$. Curved lines denote constant value contours of ${\kappa }_0$. Right: temperature dependence of the ratio of Hall-like thermal conductivity ${\overline{\kappa }}_1$ and ${\overline{\kappa }}_1+{\overline{\kappa }}_2$ to ${\kappa }_0$, for two different choices of magnetic field at $\mu =100\mathrm{MeV}$.

Figure 3

The temperature behavior of Knudsen number $Kn$ for various values of magnetic field decay parameter, ${\tau }_B=2$, 3, 6 fm at $\mu =100\mathrm{MeV}$.

Figure 4

Elliptic flow $v_2$ as a function of multiplicity. The result is compared with that from [63]. Inset plot: the temperature dependence of $v_2$ for various magnetic field decay parameter values, ${\tau }_B=2$, 3, 6 fm at $\mu =100\mathrm{MeV}$.

Figure 5

The relative significance of thermal to electric charge transport is plotted against temperature on the x-axis and chemical potential on the y-axis along two different directions, (left panel) $\frac{{\kappa }_0}{{\sigma }_{e}T}$ and (right panel) $\frac{{\kappa }_H}{{\sigma }_{H}T}$ for a constant value of magnetic field decay rate, ${\tau }_B=5\mathrm{fm}$. Curved lines denote constant value contours of depicted quantities.

Figure 6

Left: the Seebeck coefficient $S_B$ is plotted against temperature on the x-axis and chemical potential on the y-axis. Right: the same plot for Nernst coefficient $NB$. The analysis has been carried out for a constant value of magnetic field decay rate, ${\tau }_B=5\mathrm{fm}$.