Wiedemann-Franz law for hot QCD matter in a color string percolation scenario

Transport coefficients serve as important probes in characterizing the QCD matter created in high-energy heavy-ion collisions. Thermal and electrical conductivities as transport coefficients have special significance in studying the time evolution of the created matter. We have adopted a color string percolation approach for the estimation of thermal conductivity ($\kappa$), electrical conductivity (${\sigma }_{\mathrm{el}}$), and their ratio, which is popularly known as the Wiedemann-Franz law in condensed matter physics. The ratio $\kappa /{\sigma }_{\mathrm{el}}T$, which is also known as the Lorenz number ($\mathbb{L}$), is studied as a function of temperature and is compared with various theoretical calculations. We observe that the thermal conductivity for a hot QCD medium is almost temperature independent in the present formalism and matches with the results obtained in an ideal equation of state for quark-gluon plasma with a fixed coupling constant (${\alpha }_s$). The obtained Lorenz number is compared with the Stefan-Boltzmann limit for an ideal gas. We observe that a hot QCD medium with color degrees of freedom behaves like a free electron gas.

Figure 1

The dimensionless ratio of thermal conductivity to squared temperature ($\kappa /T^2$) as a function of $T/T_c$. The black solid line shows the results obtained in the CSPM. The blue diamond symbols are the calculations of the NJL model [33]. The green dotted and the red dash-dotted lines represent the results of ideal EOSs with different running coupling constants. The black, red, and green dashed lines are the results from a quasiparticle model.

Figure 2

The results for Lorenz number versus $T/T_c$ are shown for various EOSs. The black solid line shows the results calculated using the CSPM. The red solid and green dotted lines represent the results of ideal EOS for various coupling strengths. The red dash-dotted, black dotted, and blue lines are results obtained in different versions of the quasiparticle model.