Thermalization Scenario Research Articles

Jet quenching parameter in QCD kinetic theory

We study the jet quenching parameter q^ in a nonequilibrium plasma using the QCD effective kinetic theory. We discuss subleading terms at large jet momentum p, show that our expression for q^ reproduces thermal results at small and large transverse momentum cutoffs for infinite p, and construct an interpolation between these limits to be used in phenomenological applications. Using simple nonequilibrium distributions that model pertinent features of the bottom-up thermalization scenario, we analytically assess how anisotropy, underoccupation, or overoccupation affect the jet quenching parameter. Our work provides more details on the q^ formula used in our preceding work [ ] and sets the stage for further numerical studies of jet momentum broadening in the initial stages of heavy-ion collisions from QCD kinetic theory. Published by the American Physical Society 2024

Limiting attractors in heavy-ion collisions

We study universal features of the hydrodynamization process in heavy-ion collisions using QCD kinetic theory simulations for a wide range of couplings. We introduce the new concept of limiting attractors, which are obtained by extrapolation to vanishing and strong couplings. While the hydrodynamic limiting attractor emerges at strong couplings and is governed by the viscosity-related relaxation time scale τR, we identify a bottom-up limiting attractor at weak couplings. It corresponds to the late stages of the perturbative bottom-up thermalization scenario and exhibits isotropization on the time scale τBMSS=αs−13/5/Qs. In contrast to hydrodynamic limiting attractors, at finite couplings the bottom-up limiting attractor provides a good universal description of the pre-hydrodynamic evolution of jet and heavy-quark momentum broadening ratios qˆyy/qˆzz and κT/κz. We also provide parametrizations for these ratios for phenomenological studies of pre-equilibrium effects on jets and heavy quarks.

Heavy quark momentum diffusion coefficient during hydrodynamization via effective kinetic theory

In these proceedings, we compute the heavy quark momentum diffusion coefficient using QCD effective kinetic theory for a plasma going through the bottom-up thermalization scenario until approximate hydrodynamization. This transport coefficient describes heavy quark momentum diffusion in the quark-gluon plasma and is used in many phenomenological frameworks, e.g. in the open quantum systems approach. Our extracted nonthermal diffusion coefficient matches the thermal one for the same energy density within 30%. At large occupation numbers in the earliest stage, the transverse diffusion coefficient dominates, while the longitudinal diffusion coefficient is larger for the underoccupied system in the later stage of hydrodynamization.

Hydrodynamic attractor of a hybrid viscous fluid in Bjorken flow

The nonequilibrium evolution in a boost-invariant Bjorken flow of a hybrid viscous fluid model containing two interacting components with different viscosities, such that they represent strongly and weakly self-coupled sectors, is shown to be characterized by a hydrodynamic attractor which has an early-time behavior that is reminiscent of the so-called bottom-up thermalization scenario in heavy-ion collisions. The hydrodynamization times for the two sectors can differ strongly, with details depending on the curve realized on the two-dimensional attractor surface, which might account for different scenarios for small and large systems in nuclear collisions. The total system behaves like a single viscous fluid with a dynamically determined effective shear viscosity.

Non-thermal photons from the pre-equilibrium stages

I compute the invariant yield of photons from the pre-equilibrium stage of heavy-ion collision using the ”bottom-up” thermalization scenario and scaling gluon distributions found in classical statistical lattice simulations. I find it to dominate the spectrum specially at higher values of the saturation scale . I constrain the system using charge hadron multiplicities from LHC and RHIC, where fair agreement with data is obtained. Finally, I present a comparison of the ”bottom-up” scenario to one in which a thermal stage is achieved at an early time, Qsτ ∼ 1.

Probing the evolution of heavy-ion collisions using direct photon interferometry

We investigate the measurement of Hanbury Brown-Twiss (HBT) photon correlations as an experimental tool to discriminate different sources of photon enhancement, which are proposed to simultaneously reproduce the direct photon yield and the azimuthal anisotropy measured in nuclear collisions at RHIC and the LHC. To showcase this, we consider two different scenarios in which we enhance the yields from standard hydrodynamical simulations. In the first, additional photons are produced from the early pre-equilibrium stage computed from the \textit{bottom-up} thermalization scenario. In the second, the thermal rates are enhanced close to the pseudo-critical temperature $T_c\approx 155\,\text{MeV}$ using a phenomenological ansatz. We compute the correlators for relative momenta $q_o, \,q_s$ and $q_l$ for different transverse pair momenta, $K_\perp$, and find that the longitudinal correlation is the most sensitive to different photon sources. Our results also demonstrate that including anisotropic pre-equilibrium rates enhances non-Gaussianities in the correlators, which can be quantified using the kurtosis of the correlators. Finally, we study the feasibility of measuring a direct photon HBT signal in the upcoming high-luminosity LHC runs. Considering only statistical uncertainties, we find that with the projected $\sim 10^{10}$ heavy ion events a measurement of the HBT correlations for $K_\perp<1\, \text{GeV}$ is statistically significant.

Theory of Bose condensation of light via laser cooling of atoms.

A Bose-Einstein condensate (BEC) is a quantum phase of matter achieved at low temperatures. Photons, one of the most prominent species of bosons, do not typically condense due to the lack of a particle number conservation. We recently described a photon thermalization mechanism which gives rise to a grand canonical ensemble of light with effective photon number conservation between a subsystem and a particle reservoir. This mechanism occurs during Doppler laser cooling of atoms where the atoms serve as a temperature reservoir while the cooling laser photons serve as a particle reservoir. In contrast to typical discussions of BEC, our system is better treated with a controlled chemical potential rather than a controlled particle number, and is subject to energy-dependent loss. Here, we address the question of the possibility of a BEC of photons in this laser cooling photon thermalization scenario and theoretically demonstrate that a Bose condensation of photons can be realized by cooling an ensemble of two-level atoms (realizable with alkaline-earth atoms) inside a Fabry-Pérot cavity.

Photons from thermalizing matter in heavy ion collisions

We investigate the production of direct photons in heavy ion collisions within the modified bottom–up thermalization scenario, which we show to be related to the thermalizing Glasma framework. The dynamics of the parton system up to thermalization/equilibration can be described by two momentum scales, by means of which we express the photon invariant yield excluding the prompt pQCD contribution. We derive an analytic formula, which provides an estimate of photon production from thermalizing matter for a wide range of collision systems and energies. We compare the yield with that measured in the PHENIX Au+Au run04 and the combined run07+run10 data sets at sNN=200GeV. We also make theory-data comparisons for Pb+Pb at 2760 GeV and d+Au at 200 GeV collision energies. Finally, we make predictions for the direct photon invariant yield from collisions of U+U, Cu+Au, He3+Au at 200 GeV and Pb+Pb at 5020 GeV.

Nonequilibrium quark production in the expanding QCD plasma

We perform real-time lattice simulations of nonequilibrium quark production in the longitudinally expanding QCD plasma. Starting from a highly occupied gluonic state with vacuum quark sector, we extract the time evolution of quark and gluon number densities per unit transverse area and rapidity. The total quark number shows after an initial rapid increase an almost linear growth with time. Remarkably, this growth rate appears to be consistent with a simple kinetic theory estimate involving only two-to-two scattering processes in small-angle approximation. This extends previous findings about the role of two-to-two scatterings for purely gluonic dynamics in accordance with the early stages of the bottom-up thermalization scenario.

How brightly does the Glasma shine? Photon production off-equilibrium

We present a parametric estimate of photon production at early times in heavy-ion collisions based on a consistent weak coupling thermalization scenario. We quantify the contribution of the off-equilibrium Glasma phase relative to that of a thermalized Quark-Gluon Plasma. Taking into account the constraints from charged hadron multiplicity data, the Glasma contribution is found to be significant especially for large values of the saturation scale.

Thermalization of noninteracting quantum systems coupled to blackbody radiation: A Lindblad-based analysis

We study the thermalization of an ensemble of $N$ elementary, arbitrarily-complex, quantum systems, mutually noninteracting but coupled as electric or magnetic dipoles to a blackbody radiation. The elementary systems can be all the same or belong to different species, distinguishable or indistinguishable, located at fixed positions or having translational degrees of freedom. Even if the energy spectra of the constituent systems are nondegenerate, as we suppose, the ensemble unavoidably presents degeneracies of the energy levels and/or of the energy gaps. We show that, due to these degeneracies, a thermalization analysis performed by the popular quantum optical master equation reveals a number of serious pathologies, possibly including a lack of ergodicity. On the other hand, a consistent thermalization scenario is obtained by introducing a Lindblad-based approach, in which the Lindblad operators, instead of being derived from a microscopic calculation, are established as the elements of an operatorial basis with squared amplitudes fixed by imposing a detailed balance condition and requiring their correspondence with the dipole transition rates evaluated under the first-order perturbation theory. Due to the above-mentioned degeneracies, this procedure suffers a basis arbitrariness which, however, can be removed by exploiting the fact that the thermalization of an ensemble of noninteracting systems cannot depend on the ensemble size. As a result, we provide a clear-cut partitioning of the thermalization time into dissipation and decoherence times, for which we derive formulas giving the dependence on the energy levels of the elementary systems, the size $N$ of the ensemble, and the temperature of the blackbody radiation.

Effective kinetic description of the expanding overoccupied glasma

We report on a numerical study of the Boltzmann equation including $2\leftrightarrow 2$ scatterings of gluons and quarks in an overoccupied Glasma undergoing longitudinal expansion. We find that when a cascade of gluon number to the infrared occurs, corresponding to an infrared enhancement analogous to a transient Bose-Einstein condensate, gluon distributions qualitatively reproduce the results of classical-statistical simulations for the expanding Glasma. These include key features of the distributions that are not anticipated in the "bottom-up" thermalization scenario. We also find that quark distributions, like those of gluons, satisfy self-similar scaling distributions in the overoccupied Glasma. We discuss the implications of these results for a deeper understanding of the self-similarity and universality of parton distributions in the Glasma.

Parametric estimate of the relative photon yields from the glasma and the quark-gluon plasma in heavy-ion collisions

Recent classical-statistical numerical simulations have established the "bottom-up" thermalization scenario of Baier et al. as the correct weak coupling effective theory for thermalization in ultrarelativistic heavy-ion collisions. We perform a parametric study of photon production in the various stages of this bottom-up framework to ascertain the relative contribution of the off-equilibrium "Glasma" relative to that of a thermalized Quark-Gluon Plasma. Taking into account the constraints imposed by the measured charged hadron multiplicities at RHIC and the LHC, we find that Glasma contributions are important especially for large values of the saturation scale at both energies. These non-equilibrium effects should therefore be taken into account in studies where weak coupling methods are employed to compute photon yields.

Universal attractor in a highly occupied non-Abelian plasma

We study the thermalization process in highly occupied non-Abelian plasmas at weak coupling. The non-equilibrium dynamics of such systems is classical in nature and can be simulated with real-time lattice gauge theory techniques. We provide a detailed discussion of this framework and elaborate on the results reported in~\cite{Berges:2013eia} along with novel findings. We demonstrate the emergence of universal attractor solutions, which govern the non-equilibrium evolution on large time scales both for non-expanding and expanding non-Abelian plasmas. The turbulent attractor for a non-expanding plasma drives the system close to thermal equilibrium on a time scale $t\sim Q^{-1} \alpha_s^{-7/4}$. The attractor solution for an expanding non-Abelian plasma leads to a strongly interacting albeit highly anisotropic system at the transition to the low-occupancy or quantum regime. This evolution in the classical regime is, within the uncertainties of our simulations, consistent with the ``bottom up'' thermalization scenario~\cite{Baier:2000sb}. While the focus of this paper is to understand the non-equilibrium dynamics in weak coupling asymptotics, we also discuss the relevance of our results for larger couplings in the early time dynamics of heavy ion collision experiments.

Basin of attraction for turbulent thermalization and the range of validity of classical-statistical simulations

Different thermalization scenarios for systems with large fields have been proposed in the literature based on classical-statistical lattice simulations approximating the underlying quantum dynamics. We investigate the range of validity of these simulations for condensate driven as well as fluctuation dominated initial conditions for the example of a single component scalar field theory. We show that they lead to the same phenomenon of turbulent thermalization for the whole range of (weak) couplings where the classical-statistical approach is valid. In the turbulent regime we establish the existence of a dual cascade characterized by universal scaling exponents and scaling functions. This complements previous investigations where only the direct energy cascade has been studied for the single component theory. A proposed alternative thermalization scenario for stronger couplings is shown to be beyond the range of validity of classical-statistical simulations.

Turbulent thermalization process in heavy-ion collisions at ultrarelativistic energies

The non-equilibrium evolution of heavy-ion collisions is studied in the limit of weak coupling at very high energy employing lattice simulations of the classical Yang-Mills equations. Performing the largest classical-statistical simulations to date, we find that the dynamics of the longitudinally expanding plasma becomes independent of the details of the initial conditions. After a transient regime dominated by plasma instabilities and free streaming, the subsequent space-time evolution is governed by a nonthermal fixed point, where the system exhibits the self-similar dynamics characteristic of wave turbulence. This allows us to distinguish between different kinetic scenarios in the classical regime. Within the accuracy of our simulations, the scaling behavior found is consistent with the ``bottom-up" thermalization scenario.

Formula omitted] and [formula omitted] violation and new thermalization scenario in heavy ion collisions

The violation of local P and CP invariance in QCD has been a subject of intense discussions for the last couple of years as a result of very interesting ongoing results coming from RHIC. Separately, a new thermalization scenario for heavy ion collisions through the event horizon as a manifestation of the Unruh effect, has been also suggested. In this paper we argue that these two, naively unrelated phenomena, are actually two sides of the same coin as they are deeply rooted into the same fundamental physics related to some very nontrivial topological features of QCD. We formulate the universality conjecture for P and CP odd effects in heavy ion collisions analogous to the universal thermal behaviour observed in all other high energy interactions.

Reply to “Comment on ‘Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined’ ”

In his Comment [see preceding Comment, Phys. Rev. A 82, 037601 (2010)] on the paper by Roux [Phys. Rev. A 79, 021608(R) (2009)], Rigol argued that the energy distribution after a quench is not related to standard statistical ensembles and cannot explain thermalization. The latter is proposed to stem from what he calls the eigenstate thermalization hypothesis and which boils down to the fact that simple observables are expected to be smooth functions of the energy. In this Reply, we show that there is no contradiction or confusion between the observations and discussions of Roux and the expected thermalization scenario discussed by Rigol. In addition, we emphasize a few other important aspects, in particular the definition of temperature and the equivalence of ensemble, which are much more difficult to show numerically even though we believe they are essential to the discussion of thermalization. These remarks could be of interest to people interested in the interpretation of the data obtained on finite-size systems.

Instabilities of an anisotropically expanding non-Abelian plasma:1D+3Vdiscretized hard-loop simulations

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 undergoing longitudinal free-streaming expansion. In this first real-time lattice simulation we consider the most unstable modes, long-wavelength coherent color fields that are constant in transverse directions and which therefore are effectively 1+1 dimensional in space-time, except for the auxiliary fields which also depend on discretized momentum rapidity and transverse velocity components. We reproduce the semianalytical results obtained previously for the Abelian regime, and we determine the nonlinear effects which occur when the instabilities have grown such that non-Abelian interactions become important.

Quantum Black Holes and Thermalization in Relativistic Heavy Ion Collisions

A new thermalization scenario for heavy ion collisions is discussed. It is based on the Hawking--Unruh effect: an observer moving with an acceleration $a$ experiences the influence of a thermal bath with an effective temperature $T = a / 2\pi$, similar to the one present in the vicinity of a black hole horizon. In the case of heavy ion collisions, the acceleration is caused by a pulse of chromo--electric field $E \sim Q_s^2/g$ ($Q_s$ is the saturation scale, and $g$ is the strong coupling), the typical acceleration is $a \sim Q_s$, and the heat bath temperature is $T \simeq Q_s / 2\pi \sim 200$ MeV. In nuclear collisions at sufficiently high energies the effect can induce a rapid thermalization over the time period of $\tau \sim \pi/Q_s $ accompanied by phase transitions. A specific example of chiral symmetry restoration induced by the chromo--electric field is considered; it is mathematically analogous to the phase transition occurring in the vicinity of a black hole.