# Transport coefficients of two-flavor quark matter from the Kubo formalism

## TL;DR

This paper calculates the transport coefficients of two-flavor quark matter at finite temperature and density using the Kubo formalism within the NJL model, revealing their temperature dependence and universal ratios near the Mott temperature.

## Contribution

It provides a detailed computation of thermal, electrical conductivities, and shear viscosity of quark matter, incorporating meson-exchange effects and spectral functions, with new insights into their temperature and density behavior.

## Key findings

- Conductivities decrease with temperature and density above T_M
- Universal dependence of coefficients on T/T_M across densities
- Violation of Wiedemann-Franz law and bounds on ratios like η/s

## Abstract

The transport coefficients of quark matter at non-zero chemical potential and temperature are computed within the two-flavor Nambu--Jona-Lasinio model. We apply the Kubo formalism to obtain the thermal ($\kappa$) and electrical ($\sigma$) conductivities as well as an update of the shear viscosity ($\eta$) by evaluating the corresponding equilibrium two-point correlation functions to leading order in the $1/N_c$ expansion. The Dirac structure of the self-energies and spectral functions is taken into account as these are evaluated from the meson-exchange Fock diagrams for on-mass-shell quarks. We find that the thermal and electrical conductivities are decreasing functions of temperature and density above the Mott temperature $T_{\rm M}$ of dissolution of mesons into quarks, the main contributions being generated by the temporal and vector components of the spectral functions. The coefficients show a universal dependence on the ratio $T/T_{\rm M}$ for different densities, i.e., the results differ by a chemical-potential dependent constant. We also show that the Wiedemann-Franz law for the ratio $\sigma/\kappa$ does not hold. The ratio $\eta/s $, where $s$ is the entropy density, is of order of unity (or larger) close to the Mott temperature and, as the temperature increases, approaches the AdS/CFT bound $1/4\pi$. It is also conjectured that the ratio $\kappa T/c_V $, with $c_V$ being the specific heat, is bounded from below by $1/18$.