Study of transport properties of a hot and dense QCD matter using a novel approximation method

Abstract

We have studied the charge and the heat transport properties of a hot and dense QCD matter by solving the relativistic Boltzmann transport equation using a novel approximation method. Following the recently developed novel relaxation time approximation (RTA) model, we have proposed a novel Bhatnagar-Gross-Krook (BGK) model with a modified collision integral to carry out the aforementioned study. We have also compared our findings with the results of the novel RTA, the standard RTA and the standard BGK models. Our observation shows that the novel collision integrals for both the RTA and BGK models decrease the charge and the heat transport phenomena in the medium, as evidenced by the reduced values of the transport coefficients, such as the electrical conductivity and the thermal conductivity, when compared to the standard RTA and standard BGK models. Furthermore, certain observables, such as the thermal diffusion constant and the Lorenz number have been explored using the novel approaches of the aforesaid models. We have found an overall decreasing trend of the thermal diffusion constant with the temperature in the novel BGK model, similar to the novel RTA model, but the magnitude remains higher throughout the temperature range. However, the magnitude of the thermal diffusion constant in the proposed novel BGK model remains lower than its value in the standard BGK model. The magnitude of the Lorenz number in the novel BGK model remains higher than that in the standard BGK model, but it is lower than that in the novel RTA model. We have also observed that the Lorenz number in all cases has an increasing trend at low temperatures, showing a violation of the Wiedemann-Franz law, whereas at high temperatures, it becomes saturated. The Lorenz number remaining above unity indicates that the thermal conductivity prevails over the electrical conductivity in the aforesaid models.