Relativistic viscous hydrodynamics with angular momentum

Hydrodynamics is a general theoretical framework for describing the long-time large-distance behaviors of macroscopic physical systems.It has many important applications in various branches of physics,from cosmic expansion and galaxy/star evolutions at the very large scales to relativistic nuclear collisions at the very small scales.The core of hydrodynamics is about physical quantities protected by exact conservation laws,such as energy,momentum and conserved charges.Past hydrodynamic studies almost entirely focus on the energy–momentum conservation and charge conservation.Only very recently,there has been a rapidly increasing interest in understanding the role of angular momentum conservation in the hydrodynamic context and its implications for spin transport of underlying constituents.

Perturbation solutions of relativistic viscous hydrodynamics for longitudinally expanding fireballs

The solutions of the relativistic viscous hydrodynamics for longitudinally expanding fireballs are investig-ated with the Navier-Stokes theory and Israel-Stewart theory.The energy and the Euler conservation equations for the viscous fluid are derived in Rindler coordinates,by assuming that the longitudinal expansion effect is small.Under the perturbation assumption,an analytical perturbation solution for the Navier-Stokes approximation and numerical solutions for the Israel-Stewart approximation are presented.The temperature evolution with both shear viscous ef-fect and longitudinal acceleration effect in the longitudinal expanding framework are presented.The specific temper-ature profile shows symmetric Gaussian shape in the Rindler coordinates.Further,we compare the results from the Israel-Stewart approximation with the results from the Bjorken and the Navier-Stokes approximations,in the pres-ence of the longitudinal acceleration expansion effect.We found that the Israel-Stewart approximation gives a good description of the early stage evolutions than the Navier-Stokes theory.

Chiral magnetic effect for chiral fermion system

The chiral magnetic effect is concisely derived by employing the Wigner function approach in the chiral fermion system.Subsequently,the chiral magnetic effect is derived by solving the Landau levels of chiral fermions in detail.The second quantization and ensemble average leads to the equation of the chiral magnetic effect for righthand and lefthand fermion systems.The chiral magnetic effect arises uniquely from the contribution of the lowest Landau level.We carefully analyze the lowest Landau level and find that all righthand(chirality is+1)fermions move along the direction of the magnetic field,whereas all lefthand(chirality is-1)fermions move in the opposite direction of the magnetic field.Hence,the chiral magnetic effect can be explained clearly using a microscopic approach.