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/smin 0.3 GeV −1 in the vicinity of µ = 0.

Estimating transport coefficients in hot and dense quark matter

“…Within the Green-Kubo approach, thermal conductivity was estimated for two flavors using NJL model [46] as well as in Ref. [47] within the instanton liquid model where however the thermal conductivity saturates beyond T=150 MeV in contrast to the present result. We may remark here however that, for situations, where, e.g.…”

“…These include using kinetic theory for strongly interacting systems [43], chiral perturbation theory with a pion gas [44], the Chapman-Enskog approximation [45]; Green-Kubo approach within NJL model [46] and the instanton liquid model [47]. The results, however, vary over a wide range of values, with λ = 0.008 GeV −2 as in Ref.…”

Estimating Transport Coefficients In Hot And Dense Quark Matter

“…Within the Green-Kubo approach, thermal conductivity was estimated for two flavors using NJL model [46] as well as in Ref. [47] within the instanton liquid model where however the thermal conductivity saturates beyond T=150 MeV in contrast to the present result.…”

Thermal conductivity of hot pionic medium due to pion self-energy for πσ and πρ loops

“…To date, only a few studies have addressed calculation of thermal conductivity of the strongly interacting matter. [3][4][5][6][7][8][9][10][11][12][13][14][15][16] Their estimations collectively exhibit a band of predictions as shown in the Table 1.…”