Intense transient electric ({bf E}) and magnetic ({bf B}) fields are produced in the high energy heavy-ion collisions. The electromagnetic fields produced in such high-energy heavy-ion collisions are proposed to give rise to a multitude of exciting p
henomenon including the Chiral Magnetic Effect. We use a Monte Carlo (MC) Glauber model to calculate the electric and magnetic fields, more specifically their scalar product $bf{E}cdotbf{B}$, as a function of space-time on an event-by-event basis for the Au+Au collisions at $sqrt{s_{NN}}=200$ GeV for different centrality classes. We also calculate the same for the isobars Ruthenium and Zirconium at $sqrt{s_{NN}}=200$ GeV. In the QED sector $bf{E}cdotbf{B}$ acts as a source of Chiral Separation Effect, Chiral Magnetic Wave, etc., which are associated phenomena to the Chiral Magnetic Effect. We also study the relationships between the electromagnetic symmetry plane angle defined by $bf{E}cdotbf{B}$ ($psi_{E.B}$) and the participant plane angle $psi_{P}$ defined from the participating nucleons for the second-fifth order harmonics.
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. Su
bsequently, 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.
We investigate the effect of large magnetic fields on the $2+1$ dimensional reduced-magnetohydrodynamical expansion of hot and dense nuclear matter produced in $sqrt{s_{rm NN}}$ = 200 GeV Au+Au collisions. For the sake of simplicity, we consider the
case where the magnetic field points in the direction perpendicular to the reaction plane. We also consider this field to be external, with energy density parametrized as a two-dimensional Gaussian. The width of the Gaussian along the directions orthogonal to the beam axis varies with the centrality of the collision. The dependence of the magnetic field on proper time ($tau$) for the case of zero electrical conductivity of the QGP is parametrized following [Deng 2012], and for finite electrical conductivity following [Tuchin 2013]. We solve the equations of motion of ideal hydrodynamics for such an external magnetic field. For collisions with non-zero impact parameter we observe considerable changes in the evolution of the momentum eccentricities of the fireball when comparing the case when the magnetic field decays in a conducting QGP medium and when no magnetic field is present. The elliptic-flow coefficient $v_2$ of $pi^{-}$ is shown to increase in the presence of an external magnetic field and the increment in $v_2$ is found to depend on the evolution and the initial magnitude of the magnetic field.
We estimate the event-by-event (e-by-e) distribution of the ratio ($sigma$) of the magnetic field energy to the fluid energy density in the transverse plane of Au-Au collisions at $sqrt{s_{rm NN}}$ = 200 GeV. A Monte-Carlo (MC) Glauber model is used
to calculate the $sigma$ in the transverse plane for impact parameter b=0, 12 fm at time $tau_isim$0.5 fm. The fluid energy density is obtained by using Gaussian smoothing with two different smoothing parameter $sigma_g$=0.25 , 0.5 fm. For $b=0~rm fm$ collisions $sigma$ is found to be $ll$ 1 in the central region of the fireball and $sigmagtrsim$ 1 at the periphery. For b=12 fm collisions $sigmagtrsim$ 1. The e-by-e correlation between $sigma$ and the fluid energy density ($varepsilon$) is studied. We did not find strong correlation between $sigma$ and $varepsilon$ at the centre of the fireball, whereas they are mostly anti-correlated at the periphery of the fireball.
We have calculated the temperature dependence of shear $eta$ and bulk $zeta$ viscosities of quark matter due to quark-meson fluctuations. The quark thermal width originating from quantum fluctuations of quark-$pi$ and quark-$sigma$ loops at finite te
mperature is calculated with the formalism of real-time thermal field theory. Temperature-dependent constituent-quark and meson masses, and quark-meson couplings are obtained in the Nambu--Jona-Lasinio model. We found a non-trivial influence of the temperature-dependent masses and couplings on the Landau-cut structure of the quark self-energy. Our results for the ratios $eta/s$ and $zeta/s$, where $s$ is the entropy density (also determined in the Nambu--Jona-Lasinio model in the quasi-particle approximation), are in fair agreement with results of the literature obtained from different models and techniques. In particular, our result for $eta/s$ has a minimum very close to the conjectured AdS/CFT lower bound, $eta/s = 1/4pi$.
In the initial stage of relativistic heavy-ion collisions, strong magnetic fields appear due to the large velocity of the colliding charges. The evolution of these fields appears as a novel and intriguing feature in the fluid-dynamical description of
heavy-ion collisions. In this work, we study analytically the one-dimensional, longitudinally boost-invariant motion of an ideal fluid in the presence of a transverse magnetic field. Interestingly, we find that, in the limit of ideal magnetohydrodynamics, i.e., for infinite conductivity, and irrespective of the strength of the initial magnetization, the decay of the fluid energy density $e$ with proper time $tau$ is the same as for the time-honored Bjorken flow without magnetic field. Furthermore, when the magnetic field is assumed to decay $sim tau^{-a}$, where $a$ is an arbitrary number, two classes of analytic solutions can be found depending on whether $a$ is larger or smaller than one. In summary, the analytic solutions presented here highlight that the Bjorken flow is far more general than formerly thought. These solutions can serve both to gain insight on the dynamics of heavy-ion collisions in the presence of strong magnetic fields and as testbeds for numerical codes.
