Quantum Chromodynamics in extreme environments

In this thesis, various aspects of Quantum Chromodynamics(QCD) at extreme conditions and heavy-ion collisions phenomenology have been studies. The description of chiral charge transport in non-equilibirum conditions within the framework of kinetic theory is established. Effects of chiral anomaly are encoded in Berry curvature which affects the classical equation of motion of chiral fermions. A novel method is introduced to study the longitudinal expansion of heavy-ion collisions. By applying, for the first time in heavy-ion physics, the maximum entropy method, the longitudinal freeze-out surface is reconstructed from particle spectrum data. Insights on temperature-flow profile of the longitudinal expansion are extracted by evolving the system backward, from freeze-out time to early time, by solving the 1 + 1 ideal hydrodynamic equations analytically with initial condition fixed by the reconstructed freeze-out surface. The electrical conductivity is an important parameter characterizing the transport properties of quark-gluon plasma(QGP). The first direct estimation of the electrical conductivity of QGP based on soft photon production data with realistic hydrodynamics simulation is reported. A physically intuitive and computational convenient method to solve anomalous hydrodynamic equation of axial/vector current on top of general hydrodynamic background is developed. As an application, contribution of chiral anomaly to charge dependent pion elliptic flow as observed in experiment is simulated quantitatively. The techniques of gauge/gravity correspondence have been applied to study the relation between the electrical conductivity and other me-stable modes of the medium as well as the fate of moving charmonium in QGP.