Finite size effects on the transport coefficients of strongly interacting QCD matter

Abstract: The role of finite volume effects on the various transport coefficients of strongly interacting quark matter is analyzed in the Polyakov chiral SU(3) quark mean field model (PCQMF) at finite temperatures and chemical potentials incorporating fermionic vacuum term. Using a non-zero lower momentum cutoff and two different forms of the Polyakov loop potentials with quark back reaction, we study the following viscous properties: specific shear viscosity ($\eta/s$), normalized bulk viscosity ($\zeta_b/s$), and conductivity properties: electrical conductivity ($\sigma_{el}/T$), thermal conductivity ($\kappa/T^2$). Along with this, some essential thermodynamic quantities in the context of transport properties, such as the square of the speed of sound ($c_s^2$) and the specific heat ($c_v$) at a constant volume, are computed. Finite size effects are applied to the vacuum term and its influence on the effective quark masses, thermodynamic quantities, and transport coefficients is studied. The temperature dependence of the transport coefficients is obtained through the kinetic theory approach with the relaxation time approximation. The size of the system has been found to have significant effects on all transport coefficients. We find that all the transport coefficients increase as the size of the system is reduced. We have also studied the specific sound channel $(\eta+3\zeta_b/4)/s$ and the bulk-to-shear viscosity ratio $\zeta_b/\eta$. The effect of finite size is found to be more prominent in the transition region and vanishes at high $T$. The transition temperature $T_{\chi}$ is found to decrease as the system size (characterized by $R$) decreases. At finite chemical potentials, $T_{\chi}$ is shifted to lower values compared to the case of the vanishing chemical potential.