Strong longitudinal color flux fields will be created in the initial stage of high-energy nuclear collisions. We investigate analytically time evolution of such boost-invariant color fields from Abelian-like initial conditions, and next examine stability of the boost-invariant configurations against rapidity dependent fluctuations. We find that the magnetic background field has an instability induced by the lowest Landau level whose amplitude grows exponentially. For the electric background field there is no apparent instability although pair creations due to the Schwinger mechanism should be involved.
A homogeneous color magnetic field is known to be unstable for the fluctuations perpendicular to the field in the color space (the Nielsen-Olesen instability). We argue that these unstable modes, exponentially growing, generate an azimuthal magnetic field with the original field being in the z-direction, which causes the Nielsen-Olesen instability for another type of fluctuations. The growth rate of the latter unstable mode increases with the momentum p_z and can become larger than the former's growth rate which decreases with increasing p_z. These features may explain the interplay between th…
I argue that the physics of the scattering of very high energy strongly interacting particles is controlled by a new, universal form of matter, the Color Glass Condensate. This matter is the dominant contribution to the low x part of a hadron wavefunction. In collisions, this matter almost instantaneously turns into a Glasma. The Glasma initially has strong longitudinal color electric and magnetic fields, with topological charge. These fields melt into gluons. Due to instabilities, quantum noise is converted into classical turbulence, which may be responsible for the early thermalization seen …
In heavy ion collisions, transverse momentum broadening quantifies the modification of a hard probe due to interactions with the quark-gluon plasma (QGP). We calculate momentum broadening in the Glasma, which is the highly non-isotropic precursor stage of the QGP right after the collision. We show that the Glasma leads to anisotropic momentum broadening: high energy partons accumulate more momentum along the beam axis than transverse to it. The physical origin of anisotropic broadening can be traced back to differences in the shapes of chromo-electric and chromo-magnetic flux tubes in the Glas…
We present an analytic study of the physics of the glasma which is a strong classical gluon field created at early stage of high-energy heavy-ion collisions. Our analysis is based on the picture that the glasma just after the collision is made of color electric and magnetic flux tubes extending in the longitudinal direction with their diameters of the order of 1/Q_s (Q_s is the saturation scale of the colliding nuclei). We find that both the electric and magnetic flux tubes expand outwards and the field strength inside the flux tube decays rapidly in time. Next we investigate whether there exi…
We study the gluon distribution in nucleus-nucleus collisions in the framework of the Color-Glass-Condensate. Approximate analytical solutions are compared to numerical solutions of the non-linear Yang-Mills equations. We find that the full numerical solution can be well approximated by taking the full initial condition of the fields in Coulomb gauge and using a linearized solution for the time evolution. We also compare kt-factorized approximations to the full solution.
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 perform a calculation of the one- and two-point correlation functions of energy density and axial charge deposited in the glasma in the initial stage of a heavy ion collision at finite proper time. We do this by describing the initial stage of heavy ion collisions in terms of freely evolving classical fields whose dynamics obey the linearized Yang-Mills equations. Our approach allows us to systematically resum the contributions of high momentum modes that would make a power series expansion in proper time divergent. We evaluate the field correlators in the McLerran-Venugopalan model using t…
In these proceedings, we report on our numerical lattice simulations of partons traversing the boost-invariant, non-perturbative glasma as created at the early stages of collisions at RHIC and LHC. Since these highly energetic partons are produced from hard scatterings during heavy-ion collisions, they are already affected by the first stage of the medium's time evolution, the glasma, which is the pre-equilibrium precursor state of the quark-gluon plasma. We find that partons quickly accumulate transverse momentum up to the saturation momentum during the glasma stage. Moreover, we observe an i…
The early-time evolution of the system generated in ultra-relativistic heavy ion collisions is dominated by the presence of strong color fields known as Glasma fields. These can be described following the classical approach embodied in the Color Glass Condensate effective theory, which approximates QCD in the high gluon density regime. In this framework we perform an analytical first-principles calculation of the two-point correlator of the divergence of the Chern-Simons current at proper time $τ\!=\!0^+$, which characterizes the early fluctuations of axial charge density in the plane transver…
We present an analytical calculation of the covariance of the energy-momentum tensor associated to the gluon field produced in ultra-relativistic heavy ion collisions at early times, the Glasma. This object involves the two-point and single-point correlators of the energy-momentum tensor ($\langle T^{μν}(x_{\perp})T^{σρ}(y_{\perp})\rangle$ and $\langle T^{μν}(x_{\perp})\rangle$, respectively) at proper time $τ\!=\!0^+$. Our approach is based on the Color Glass Condensate effective theory, which allows us to map the fluctuations of the valence color sources in the colliding nuclei to those of t…
We present analytic results that describe the gluon field, or glasma, at very early times after a collision of relativistic heavy ions at proper time $τ=0$. We use a Colour Glass Condensate approach, and perform an expansion in $τ$. The full details of our method are described in our previous paper [1]. In this paper we present an analysis of various physical quantities that can be obtained from the energy-momentum tensor. We show that the expansion to order $τ^6$ can be trusted to about $τ=0.05$ fm. For times small enough that the expansion converges, the transverse and longitudinal pressures…
We propose a new prescription for evaluating a von Neumann entropy in the initial stage of high-energy heavy-ion collisions utilizing the time evolution of classical Yang-Mills (CYM) field: The von Neumann entropy is computed for the quantum coherent states constructed so as to give the classical gluon fields as the expectation values. The entropy is to be liberated when the complete decoherence is achieved. As a demonstration, the time evolution of the CYM dynamics is solved with an initial condition which mimics the Glasma state, though in a non-expanding geometry; the Glasma state is charac…
I review recent analytical and numerical advances in the study of non-equilibrium quark-gluon plasma physics. I concentrate on studies of the dynamics of plasmas which are locally anisotropic in momentum space. In contrast to locally isotropic plasmas such anisotropic plasmas have a spectrum of soft unstable modes which are characterized by exponential growth of transverse (chromo)-magnetic fields at short times. Parametrically the instabilities provide the fastest method for generation of soft background fields and dominate the short-time dynamics of the system.
Non-Abelian plasma instabilities play a crucial role in the nonequilibrium dynamics of a weakly coupled quark-gluon plasma and they importantly modify the standard perturbative bottom-up thermalization scenario in heavy-ion collisions. Using the auxiliary-field formulation of the hard-loop effective theory, we study numerically the real time evolution of instabilities in an anisotropic collisionless Yang-Mills plasma expanding longitudinally in free streaming. In this first real-time lattice simulation we consider the most unstable modes, long-wavelength coherent color fields that are constant…
We calculate eccentricities in high energy proton-nucleus collisions, by calculating correlation functions of the energy density field of the Glasma immediately after the collision event at proper time tau = 0. We separately consider the effects of color charge and geometrical hot spot fluctuations, analytically performing the averages over both in a dilute-dense limit. We show that geometric fluctuations of hot spots inside the proton are the dominant source of eccentricity whereas color charge fluctuations only give a negligible correction. The size and number of hot spots are the most impor…
We study the stability of a scalar inflaton field and analyze its point attractors in the phase space. We show that the value of the inflaton field in the vacuum is a bifurcation parameter and prove the possible existence of a limit cycle by using analytical and numerical arguments.
We investigate axial charge production in two-color QCD out of equilibrium. We compute the real-time evolution starting with spatially homogeneous strong gauge fields, while the fermions are in vacuum. The idealized class of initial conditions is motivated by glasma flux tubes in the context of heavy-ion collisions. We focus on axial charge production at early times, where important aspects of the anomalous dynamics can be derived analytically. This is compared to real-time lattice simulations. Quark production at early times leading to anomalous charge generation is investigated using Wilson …
The time evolution of collective modes in an expanding ultarelativistic and (effectively) Abelian plasma is studied in the hard-loop approximation semi-analytically by means of integro-differential equations. A previous treatment is generalized to arbitrary orientation of wave vectors with respect to the direction of anisotropy and thus to a fully 3+1 dimensional situation. Moreover, initial fluctuations are allowed in both gauge fields and currents, which is necessary in the case of (stable) longitudinal modes. For unstable (Weibel) modes, this generalization of initial conditions reduces dra…
