Thermal conductivity of the quark matter for the SU(2) light-flavor sector

We investigate the thermal conductivity ($\kappa$) of the quark matter at finite quark chemical potential $(\mu )$ and temperature $(T)$, employing the Green-Kubo formula, for the SU(2) light-flavor sector with the finite current-quark mass $m=5$ MeV. As a theoretical framework, we construct an effective thermodynamic potential from the $(\mu ,T)$-modified liquid-instanton model (mLIM). Note that all the relevant model parameters are designated as functions of $T$, using the trivial-holonomy caloron solution. By solving the self-consistent equation of mLIM, we acquire the constituent-quark mass $M_0$ as a function of $T$ and $\mu$, satisfying the universal-class patterns of the chiral phase transition. From the numerical results for $\kappa$, we observe that there emerges a peak at $\mu \approx 200$ MeV for the low-$T$ region, i.e. $T\lesssim 100$ MeV. As $T$ increase over $T\approx 100$ MeV, the curve for $\kappa$ is almost saturated as a function of $T$ in the order of $\sim {10}^{-1}{\mathrm{G}\mathrm{e}\mathrm{V}}^2$, and grows with respect to $\mu$ smoothly. At the normal nuclear-matter density ${\rho }_0=0.17{\mathrm{f}\mathrm{m}}^{-3}$, $\kappa$ shows its maximum $6.22{\mathrm{G}\mathrm{e}\mathrm{V}}^2$ at $T\approx 10$ MeV, then decreases exponentially down to $\kappa \approx 0.2{\mathrm{G}\mathrm{e}\mathrm{V}}^2$. We also compute the ratio of $\kappa$ and the entropy density, i.e. $\kappa \mathrm{/}s$ as a function of $(\mu ,T)$ which is a monotonically decreasing function for a wide range of $T$, then approaches a lower bound at very high $T$: $\kappa \mathrm{/}{s}_{\mathrm{m}\mathrm{i}\mathrm{n}}\gtrsim 0.3{\mathrm{G}\mathrm{e}\mathrm{V}}^{-1}$ in the vicinity of $\mu =0$.