Shear Viscosity Coefficients of Graphene and Other Systems

Abstract

In this thesis, we have conducted a detailed microscopic analysis of the shear viscosity two dimensional and three-dimensional graphene system in both the presence of magnetic field and absence of magnetic field within the framework of the kinetic theory, employing the relaxation time approximation. The derived expressions for shear viscosity were subsequently compared with those of other two-dimensional and three-dimensional non-relativistic and ultra-relativistic fluid systems. The objective of this comparison was to investigate how variations in one body dispersion relations influence many-body fluid properties, such as shear viscosity and the viscosity-to-entropy density ratio for the absence of magnetic field case. Additionally, the study aimed to elucidate the transformation of mathematical structures when transitioning from three dimensional to two-dimensional systems. Numerical analyses were performed to explore the differences in the magnitudes and dependencies of these properties on thermodynamic parameters, namely temperature and chemical potential. For the two-dimensional graphene system,distinct thermodynamic regimes were identified: the Dirac fluid and the Fermi liquid domains. newlineIt was observed that the shear viscosity, entropy density, and their ratio decrease and approach saturation as the system transitions from the Fermi liquid to the Dirac fluid domain. Extrapolating to the high-energy physics context, where temperature and chemical potential shift from millielectronvolt scales in condensed matter physics to megaelectronvolt scales, analogous results are anticipated for hot quark matter. In the part of magnetic field case, we have calculated and explored the anisotropic components of shear viscosity for graphene comparing with the non-relativistic case. Their normalised shear viscosity ratios have have been analyzed by tuning the chemical potential and temperature in the Fermi integral and the same has been done according to magnetic field. (Full abstract uploaded) newline