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 M0 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≈200 MeV for the low-T region, i.e. T≲100 MeV . As T increase over T≈100 MeV , the curve for κ is almost saturated as a function of T in the order of ~ 10-1 GeV 2, and grows with respect to μ smoothly. At the normal nuclear-matter density ρ0 = 0.17 fm -3, κ shows its maximum 6.22 GeV 2 at T≈10 MeV , then decreases exponentially down to κ≈0.2 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 min ≳0.3 GeV -1 in the vicinity of μ = 0.