Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOne particle distribution function and shear viscosity in magnetic field: a relaxation time approach
59
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We calculate the $delta f$ correction to the one particle distribution function in presence of magnetic field and non-zero shear viscosity within the relaxation time approximation. The $delta f$ correction is found to be electric charge dependent. Subsequently, we also calculate one longitudinal and four transverse shear viscous coefficients as a function of dimensionless Hall parameter $chi_{H}$ in presence of the magnetic field. We find that a proper linear combination of the shear viscous coefficients calculated in this work scales with the result obtained from Grads moment method in cite{Denicol:2018rbw}. Calculation of invariant yield of $pi^{-}$ in a simple Bjorken expansion with cylindrical symmetry shows no noticeable change in spectra due to the $delta f$ correction for realistic values of the magnetic field and relaxation time. However, when transverse expansion is taken into account using a blast wave type flow field we found noticeable change in spectra and elliptic flow coefficients due to the $delta f$ correction. The $delta f$ is also found to be very sensitive on the magnitude of magnetic field. Hence we think it is important to take into account the $delta f$ correction in more realistic numerical magnetohydrodynamics simulations.
rate research
Read More
We have studied the collisional time and relaxation time of a QGP(Quark-Gluon Plasma) by parameterizing them by temperature. From this parameterization we have obtained the decay rate parameterized by temperature which further helps us to calculate and compare the shear viscosity to entropy density ratio of a QGP with the KSS(Kovtun-Son-Starinets) result.
The microscopic formulae of the bulk viscosity $zeta $ and the corresponding relaxation time $tau_{Pi}$ in causal dissipative relativistic fluid dynamics are derived by using the projection operator method. In applying these formulae to the pionic fluid, we find that the renormalizable energy-momentum tensor should be employed to obtain consistent results. In the leading order approximation in the chiral perturbation theory, the relaxation time is enhanced near the QCD phase transition and $tau_{Pi}$ and $zeta $ are related as $tau_{Pi}=zeta /[beta {(1/3-c_{s}^{2})(epsilon +P)-2(epsilon -3P)/9}]$, where $epsilon $, $P$ and $c_{s}$ are the energy density, pressure and velocity of sound, respectively. The predicted $zeta $ and $% tau_{Pi}$ should satisfy the so-called causality condition. We compare our result with the results of the kinetic calculation by Israel and Stewart and the string theory, and confirm that all the three approaches are consistent with the causality condition.
This paper presents how thermal mean field effects are incorporated consistently in the hydrodynamical modelling of heavy-ion collisions. The nonequilibrium correction to the distribution function resulting from a temperature-dependent mass is obtained in a procedure which automatically satisfies the Landau matching condition and is thermodynamically consistent. The physics of the bulk viscosity is studied here for Boltzmann and Bose-Einstein gases within the Chapman-Enskog and 14-moment approaches in the relaxation time approximation. Constant and temperature-dependent masses are considered in turn. It is shown that, in the small mass limit, both methods lead to the same value of the ratio of the bulk viscosity over its relaxation time. The inclusion of a temperature-dependent mass leads to the emergence of the $beta_lambda$-function in that ratio, and it is of the expected parametric form for the Boltzmann gas, while for the Bose-Einstein case it is affected by the infrared cut-off. This suggests that the relaxation time approximation may be too crude to obtain a reliable form of $zeta/tau_R$ for gases obeying Bose-Einstein statistics.
Shear viscosity $eta$ is calculated for the nuclear matter described as a system of interacting nucleons with the van der Waals (VDW) equation of state. The Boltzmann-Vlasov kinetic equation is solved in terms of the plane waves of the collective overdamped motion. In the frequent-collision regime, the shear viscosity depends on the particle-number density $n$ through the mean-field parameter $a$, which describes attractive forces in the VDW equation. In the temperature region $T=15 - 40$~MeV, a ratio of the shear viscosity to the entropy density $s$ is smaller than 1 at the nucleon number density $n =(0.5 - 1.5),n^{}_0$, where $n^{}_0=0.16,$fm$^{-3}$ is the particle density of equilibrium nuclear matter at zero temperature. A minimum of the $eta/s$ ratio takes place somewhere in a vicinity of the critical point of the VDW system. Large values of $eta/sgg 1$ are, however, found in both the low-density, $nll n^{}_0$, and high-density, $n>2n^{}_0$, regions. This makes the ideal hydrodynamic approach inapplicable for these densities.
Properties of equilibrated nucleon system are studied within the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) transport model. The UrQMD calculations are done within a finite box with periodic boundary conditions. The system achieves thermal equilibrium due to nucleon-nucleon elastic scattering. For the UrQMD equilibrium state, nucleon energy spectra, equation of state, particle number fluctuations, and shear viscosity $eta$ are calculated. The UrQMD results are compared with both, statistical mechanics and Chapman-Enskog kinetic theory, for a classical system of nucleons with hard-core repulsion.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
