In the present work, we investigate the effects of magnetic field on expanding hot and dense nuclear matter as an ideal fluid. We consider QGP, on the particular case of a (1 + 2) dimensional longitudinally boost-invariant fluid expansion, in the background of an inhomogeneous magnetic field that is generated by external sources. We assume the magnetic field points in the direction perpendicular to the reaction plane, follows the power-law decay in proper time, and has two components on the transverse plane. To simplify the calculation, we suppose the investigated fluid has azimuthal symmetry, and magneto-hydrodynamic equations are described in a polar coordinate system on the transverse plane of reaction. Our results depict the space-time evolution of the transverse expansion of the fluid in the presence of an inhomogeneous external magnetic field. Ultimately, we utilize transverse velocity and correction of energy density to estimate the transverse momentum spectrum of final particles that emerge from heavy-ion collisions based on experimental data.
We investigate the leading twist quark generalized transverse momentum distributions (GTMDs) at nonzero skewness in a light-front quark-diquark model for the nucleon motivated by soft-wall AdS/QCD. The boost-invariant longitudinal coordinate, $σ=\frac{1}{2} b^- P^+$, is identified as the Fourier conjugate of the skewness. The Fourier transform of the GTMDs with respect to the skewness variable $ξ$ can be employed to provide the Wigner distributions in the boost-invariant longitudinal position space $σ$, the coordinate conjugate to light-front time, $τ=t+z/c$. The Wigner distributions in the lo…
We study relativistic magnetohydrodynamics with longitudinal boost invariance in the presence of chiral magnetic effects and finite electric conductivity. With initial magnetic fields parallel or anti-parallel to electric fields, we derive the analytic solutions of electromagnetic fields and the chiral number and energy density in an expansion of several parameters determined by initial conditions. The numerical solutions show that such analytic solutions work well in weak fields or large chiral fluctuations. We also discuss the properties of electromagnetic fields in the laboratory frame.
We study the evolution of the longitudinal expansion of an ideal fluid with finite electrical conductivity, which is subject to the EM fields. In the framework of resistive relativistic-magneto-hydrodynamic, we find an exact analytical solution for the EM fields and for the acceleration of the fluid.
We simulate the 3+1 D classical Yang-Mills dynamics of the collisions of longitudinally extended nuclei, described by eikonal color charges in the Color Glass Condensate framework. By varying the longitudinal thickness of the colliding nuclei, we discuss the violations of boost invariance and explore how the boost invariant high-energy limit is approached. Subsequently, we develop a more realistic model of the three dimensional color charge distributions that connects longitudinal and transverse fluctuations to the $x$ and $k_\bot$ dependence of transverse momentum dependent parton distributio…
Non-central heavy-ion collisions generate the strongest magnetic field of the order of $10^{18}-10^{19}$ Gauss due to the electric current produced by the positively charged spectators that travel at nearly the speed of light. Such transient electromagnetic fields may induce various novel effects in the hydrodynamic description of the quark gluon plasma for non-central heavy-ion collisions. We investigate the longitudinal acceleration effects on the 1+1 dimensional relativistic magnetohydrodynamics with transverse magnetic fields. We analyze the proper time evolution of the system energy densi…
Using Monte Carlo generators of the PYTHIA model for hadron-hadron collisions and a multi-phase transport (AMPT) model for nucleus-nucleus collisions, the longitudinal boost-invariance of charge balance function and its transverse momentum dependence are carefully studied. It shows that the charge balance function is boost-invariant in both {\it p}+{\it p} and Au+Au collisions in these two models, consistent with experimental data. The balance function properly scaled by the width of the pseudorapidity window is independent of the position or the size of the window and is corresponding to the …
We investigate three-dimensional ideal hydrodynamic evolution, with Landau initial conditions, incorporating event-by-event variation with many events and transverse density inhomogeneities. We show that the transition to boost-invariant flow occurs too late for realistic setups, with corrections of $\order{20-30\%}$ expected at freezeout for most scenarios. Moreover, the deviation from boost-invariance is correlated with both transverse flow and elliptic flow, with the more highly transversely flowing regions also showing the most violation of boost invariance. Therefore, if longitudinal flow…
We study the kinetic freeze out conditions of bulk hadrons in nuclear collisions. The transverse and longitudinal momentum spectra of the identified hadrons produced in central Au+Au and Pb+Pb collisions, in the beam energy range of $E_b = 2A - 158 A$ GeV are analysed for this purpose, within a generalised non boost-invariant blast wave model. The kinetic freeze out temperature is found to vary in the range of 55 - 90 MeV, whereas the average transverse velocity of collective expansion is found to be around $0.5c$ to $0.6c$. The mean longitudinal velocity of the fireball is seen to increase mo…
We study the polarization of particles in relativistic heavy-ion collisions at very high energy along the beam direction within a relativistic hydrodynamic framework. We show that this component of the polarization decreases much slower with center-of-mass energy compared to the transverse component, even in the ideal longitudinal boost-invariant scenario with non-fluctuating initial state, and that it can be measured by taking advantage of its quadrupole structure in the transverse momentum plane. In the ideal longitudinal boost-invariant scenario, the polarization is proportional to the grad…
We present our progress on simulating the Glasma in the early stages of heavy ion collisions in a non-boost-invariant setting. Our approach allows us to describe colliding nuclei with finite longitudinal width by extending the McLerran-Venugopalan model to include a parameter for the Lorentz-contracted but finite extent of the nucleus in the beam direction. We determine the rapidity profile of the Glasma energy density, which shows strong deviations from the boost invariant result. Both broad and narrow profiles can be produced by varying the initial conditions. We find reasonable agreement wh…
We consider the longitudinal hydrodynamic evolution of the fireball created in a relativistic heavy-ion collision. Nonzero shear viscosity reduces the colling rate of the system and hinders the acceleration of the longitudinal flow. As a consequence, the initial energy density needed to reproduce the experimental data at RHIC energies is significantly reduced. At LHC energies, we expect that shear viscosity helps to conserve a Bjorken plateau in the rapidity distributions during the expansion.
We study the dynamics of nonequilibrium instabilities in anisotropically expanding systems. The most prominent example of such a system is the 'Glasma' in the context of relativistic heavy-ion collision experiments, where the expansion is a consequence of approximately boost-invariant initial conditions. Here we consider the problem of parametric resonance in scalar $N$-component quantum field theories with boost-invariant initial conditions, which is similar in spirit. We find that many aspects of the dynamics can be treated analytically by introducing a generalized conformal time. Primary in…
We present a new solution of relativistic hydrodynamics in 1+3 dimensions which depends on both the transverse coordinate and rapidity. At early times the flow expands dominantly longitudinally in a non-boost-invariant manner, and at late times it expands nearly spherically. These two regimes are shown to be related by symmetry. The effect of viscosity is also discussed.
A formalism for anisotropic fluid dynamics is proposed. It is designed to describe boost-invariant systems with anisotropic pressure. Such systems are expected to be produced at the early stages of relativistic heavy-ion collisions, when the timescales are too short to achieve equal thermalization of transverse and longitudinal degrees of freedom. The approach is based on the energy-momentum and entropy conservation laws, and may be regarded as a minimal extension of the boost-invariant standard relativistic hydrodynamics of the perfect fluid. We show how the formalism may be used to describe …
We investigate the electromagnetic form factor $F(q^2)$ of the meson by using the solvable $ϕ^{3}$ scalar field model in $(1+1)$ dimensions. As the transverse rotations are absent in $(1+1)$ dimensions, the advantage of the light-front dynamics (LFD) with the light-front time $x^+ = x^0 + x^3$ as the evolution parameter is maximized in contrast to the usual instant form dynamics (IFD) with the ordinary time $x^0$ as the evolution parameter. In LFD, the individual $x^+$-ordered amplitudes contributing to $F(q^2)$ are invariant under the boost, i.e., frame-independent, while the individual $x^0$…
We investigate hydrodynamic evolution of the quark gluon plasma for the colour glass condensate type initial conditions. We solve full second-order viscous hydrodynamic equations in the longitudinal direction to find that non-boost invariant expansion leads to visible deformation on the initial rapidity distribution. The results indicate that hydrodynamic evolution with viscosity plays an important role in determining parameters for the initial distributions.
At strong coupling holographic studies have shown that heavy ion collisions do not obey normal boost invariance. Here we study a modified boost invariance through a complex shift in time, and show that this leads to surprisingly good agreement with numerical holographic computations. When including perturbations the agreement becomes even better, both in the hydrodynamic and the far-from-equilibrium regime. One of the main advantages is an analytic formulation of the stress-energy tensor of the longitudinal dynamics of holographic heavy ion collisions.
We study anomalous magnetohydrodynamics in a longitudinal boost invariant Bjorken flow with constant anisotropic electric conductivities as outlined in Ref. [1]. For simplicity, we consider a neutral fluid and a force-free magnetic field in the transverse direction. We derived analytic solutions of the electromagnetic fields in the laboratory frame, the chiral density, and the energy density as functions of proper time.
We consider dissipative phenomena due to the relaxation of an initial anisotropic local pressure in the fireball created in relativistic heavy-ion collisions, both for the Bjorken boost-invariant case and for the azimuthally symmetric radial expansion with boost-invariance. The resulting increase of the entropy can be counterbalanced by a suitable retuning of the initial temperature. An increase of the transverse collective flow is observed. The influence of the shear viscosity on the longitudinal expansion is also studied. Viscosity reduces the cooling rate from the longitudinal work and coun…
We formulate a general theory of thermal fluctuations within causal second-order viscous hydrodynamic evolution of matter formed in relativistic heavy-ion collisions. The fluctuation is treated perturbatively on top of a boost-invariant longitudinal expansion. Numerical simulation of thermal noise is performed for a lattice QCD equation of state and for various second-order dissipative evolution equations. Phenomenological effects of thermal fluctuations on the two-particle rapidity correlations are studied.
Simple, self-similar, analytic solutions of 1 + 1 dimensional relativistic hydrodynamics are presented, generalizing the Hwa - Bjorken boost-invariant solution to inhomogeneous rapidity distributions. These solutions are generalized also to 1 + 3 dimensional, cylindrically symmetric firetubes, corresponding to central collisions of heavy ions at relativistic bombarding energies.
We study the effects of hydrodynamic fluctuations in non-boost-invariant longitudinal expansion of matter formed in relativistic heavy ion collisions. We formulate the theory of thermal noise within second-order viscous hydrodynamics treating noise as a perturbation on top of the non-boost-invariant flow. We develop a numerical simulation model to treat the (1+1)-dimension hydrodynamic evolution. The code is tested to reproduce the analytic results for the Riemann solver for expansion of matter in vacuum. For viscous hydrodynamic expansion, the initial energy density distribution are obtained …
We propose several new observables/correlators, based on correlations between two or more subevents separated in pseudorapidity $η$, to study the longitudinal flow fluctuations. We show that these observables are sensitive to the event-by-event fluctuations, as a function of $η$, of the initial condition as well as the non-linear mode-mixing effects. Experimental measurement of these observables shall provide important new constraints on the boost-variant event-by-event initial conditions required by all 3+1-dimensional viscous hydrodynamics models.
