Shear viscosity and electric conductivity of quark matter at finite temperature and chemical potential with QCD phase transitions

In the beam energy scan phase II experiments at the Relativistic Heavy Ion Collider solenoidal tracker, the quark-gluon plasma (QGP) produced with changing collision energies may probe different regions of the QCD phase diagram. Correspondingly, studying the transport coefficients of quark matter in these regions will contribute to extracting the QCD phase structure through hydrodynamic approaches. We investigate the shear viscosity and electric conductivity within the framework of kinetic theory with the relaxation time approximation, in particular their behaviors near the Mott and first-order phase transitions with a spinodal structure as well as along the isentropic trajectories. To derived the scattering cross section under different conditions, the temperature- and chemical-potential-dependent masses of quarks, antiquarks and exchanged mesons are calculated in the Polyakov-loop extended Nambu–Jona-Lasinio model. The numerical results indicate that, at small chemical potential, the shear viscosity to entropy density ratio ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>η</a:mi> <a:mo>/</a:mo> <a:mi>s</a:mi> </a:math> ) has a minimum near the Mott phase transition and increases rapidly in the lower-temperature side of the chiral crossover phase transition. At large chemical potential (high baryon density), <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>η</c:mi> <c:mo>/</c:mo> <c:mi>s</c:mi> </c:math> in the QGP phase is dominated by temperature, and the value of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>η</e:mi> <e:mo>/</e:mo> <e:mi>s</e:mi> </e:math> is greatly enhanced at low temperatures. At intermediate temperature and chemical potential near the QCD phase transition, the behavior of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>η</g:mi> <g:mo>/</g:mo> <g:mi>s</g:mi> </g:math> is influenced by the competition between temperature, density, and QCD phase transition. The electric conductivity ( <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>σ</i:mi> <i:mo>/</i:mo> <i:mi>T</i:mi> </i:math> ) roughly exhibits similar characteristics to <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>η</k:mi> <k:mo>/</k:mo> <k:mi>s</k:mi> </k:math> in the QCD phase diagram, whereas the dimensionless ratio of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>η</m:mi> <m:mo>/</m:mo> <m:mi>s</m:mi> </m:math> to <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>σ</o:mi> <o:mo>/</o:mo> <o:mi>T</o:mi> </o:math> decreases monotonically with growing temperature, approaching a constant in the high-temperature limit.