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

Abstract

We investigate the thermal conductivity ($κ$) of the quark matter at finite quark chemical potential $(μ)$ 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 $(μ,T)$-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 $μ$, satisfying the universal-class patterns of the chiral phase transition. From the numerical results for $κ$, we observe that there emerges a peak at $μ\approx200$ MeV for the low-$T$ region, i.e. $T\lesssim100$ MeV. As $T$ increase over $T\approx100$ MeV, the curve for $κ$ is almost saturated as a function of $T$ in the order of $\sim10^{-1}\,\mathrm{GeV}^2$, and grows with respect to $μ$ smoothly. At the normal nuclear-matter density $ρ_0=0.17\,\mathrm{fm}^{-3}$, $κ$ shows its maximum $6.22\,\mathrm{GeV}^2$ at $T\approx10$ MeV, then decreases exponentially down to $κ\approx0.2\,\mathrm{GeV}^2$. We also compute the ratio of $κ$ and the entropy density, i.e. $κ/s$ as a function of $(μ,T)$ which is a monotonically decreasing function for a wide range of $T$, then approaches a lower bound at very high $T$: $κ/s_\mathrm{min}\gtrsim0.3\,\mathrm{GeV}^{-1}$ in the vicinity of $μ=0$.