Study of Hydrodynamical Behaviour and Transport Properties of Hot QCD Medium

Abstract

The primary focus of this thesis is two-fold: a) Studying the linearly stable and causal theory of relativistic third-order viscous hydrodynamics, b) A comprehensive investigation of the charge, heat, and momentum response in a hot QCD medium (called quark gluon plasma (QGP)) in the presence of a weak background constant magnetic field. A novel state of quark matter (deconfined soup of quarks and gluons) is expected to form at extremely high temperature and/or density during the ultra-relativistic heavy-ion collisions (URHICs). Under such extreme conditions, quark matter may approach local thermodynamic equilibrium, allowing the exploration of various phases as well as thermodynamic and transport properties of hot QCD medium. Determining the transport properties of this hot QCD medium formed from heavy-ion collisions (HICs) is challenging due to the lack of direct observation. Experimentally, only the energy and momenta of the particles generated in the final stages of a collision after hadronization can be observed, by which time the hot hadronic matter has cooled and become non-interacting. Therefore, to investigate the thermodynamic and transport properties of the hot QCD medium, it is necessary to model the entire heavy-ion collision process from beginning to end. The dynamic evolution of the deconfined hot QCD medium and the subsequent hot hadronic matter can be characterised using the laws of fluid dynamics, assuming that the system stays near local thermodynamic equilibrium during its evolution. Fluid dynamics, also referred to as hydrodynamics, is an effective technique for describing a system using macroscopic variables such as local energy density, pressure, temperature, and flow velocity. The earliest theoretical formulation of relativistic first- and ix x second-order dissipative hydrodynamics is well established. In the present thesis, we have formulated a linearly stable and causal theory of relativistic third-order viscous hydrodynamics from the kinetic theory in relaxation-time approximation (RTA). We have used the Chapman-Enskog-like iterative approach to solve the Boltzmann equation and obtain the dissipative correction to the distribution function. We have also demonstrated the linear stability and causality of the present formulation by considering perturbations around a global equilibrium state.