Francois Gelis
We use kinetic theory in order to study the role of quantum fluctuations in the isotropization of the pressure tensor in a system subject to fast longitudinal expansion, such as the matter produced in the early stages of a heavy ion collision.
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Bose-Einstein correlations and momentum distributions are calculated for longitudinally expanding systems, like jets or high energy heavy ion collisions with light projectiles. The expansion generates a thermal length-scale in the longitudinal direction, and the geometrical length-scale is also finite. The Bose-Einstein correlation functions are dominated by the smaller while the invariant momentum distribution by the longer of the two longitudinal length-scales.
We report on the discovery of new analytical solutions of the equations of relativistic ideal hydrodynamics. In this solution, the fluid expands in the longitudinal direction and contains a plateau structure that extends over a finite range in rapidity and can be either symmetric or asymmetric in that variable. We further calculate the corresponding pseudo-rapidity distribution of hadron yields, and find decent agreement with experimental measurements in high-energy Pb+Pb, Au+Au, p+Pb, and d+Au collisions.
A simple kinematical argument suggests that the classical approximation may be inadequate to describe the evolution of a system with an anisotropic particle distribution. In order to verify this quantitatively, we study the Boltzmann equation for a longitudinally expanding system of scalar particles interacting with a $ϕ^4$ coupling, that mimics the kinematics of a heavy ion collision at very high energy. We consider only elastic $2\to 2$ scatterings, and we allow the formation of a Bose-Einstein condensate in overpopulated situations by solving the coupled equations for the particle distribut…
Study of a longitudinally expanding plasma with the 2PI effective action
本研究首次利用双粒子不可约（2PI）有效作用量，探讨重离子碰撞中经历纵向膨胀的远离平衡介质的热化问题，计算了准粒子动量分布并证实了各向同性化的发生。
Simple, self-similar, analytic solutions of 1+1 dimensional relativistic hydrodynamics are presented, generalizing Bjorken's solution to inhomogeneous rapidity distribution.
We present new, exact, finite solutions of relativistic hydrodynamics for longitudinally expanding fireballs for arbitrary constant value of the speed of sound. These new solutions generalize earlier, longitudinally finite, exact solutions, from an unrealistic to a reasonable equation of state, characterized by a temperature independent (average) value of the speed of sound. Observables like the rapidity density and the pseudorapidity density are evaluated analytically, resulting in simple and easy to fit formulae that can be matched to the high energy proton-proton and heavy ion collision dat…
Isotropization of a longitudinally expanding system of scalar fields in the 2PI formalism
本文利用 2PI 有效作用量框架研究纵向膨胀标量场系统的各向同性化，通过数值求解运动方程，在最大耦合下观察到占据数和有效质量动量依赖的各向同性化起始。
In Phys. Rev. Lett. 114 (2015) 6, 061601, we reported on a new universality class for longitudinally expanding systems, encompassing strongly correlated non-Abelian plasmas and $N$-component self-interacting scalar field theories. Using classical-statistical methods, we showed that these systems share the same self-similar scaling properties for a wide range of momenta in a limit where particles are weakly coupled but their occupancy is high. Here we significantly expand on our previous work and delineate two further self-similar regimes. One of these occurs in the deep infrared (IR) regime of…
We use the Hamiltonian formulation of kinetic theory to perform a stability analysis of non-thermal fixed points in a non-Abelian plasma. We construct a perturbative expansion of the Fokker-Planck collision kernel in an adiabatic approximation and show that the (next-to-)leading order solutions reproduce the known non-thermal fixed point scaling exponents. Working at next-to-leading order, we derive the stability equations for scaling exponents and find the relaxation rate to the non-thermal fixed point. This approach provides the basis for an understanding of the prescaling phenomena observed…
In a series of previous papers, we have presented a new approach, based on perturbative QCD, for the evolution of a jet in a dense quark-gluon plasma. In the original formulation, the plasma was assumed to be homogeneous and static. In this work, we extend our description and its Monte Carlo implementation to a plasma obeying Bjorken longitudinal expansion. Our key observation is that the factorisation between vacuum-like and medium-induced emissions, derived in the static case, still holds for an expanding medium, albeit with modified rates for medium-induced emissions and transverse momentum…
In two previous works [arXiv:1009.4363,arXiv:1107.0668], we studied the time evolution of a system of real scalar fields with quartic coupling which shares important features with the Color Glass Condensate description of heavy ion collisions. Our primary objective was to understand how such a system, when initialized with a non-perturbatively large classical field configuration, reaches thermal equilibrium. An essential goal of these works was to highlight the role played by the quantum fluctuations. However, these studies considered only a system confined within a box of fixed volume. In the…
In-medium gluon radiation spectrum with all-order resummation of multiple scatterings in longitudinally evolving media
本文将全重和胶子谱的数值计算扩展至纵向膨胀介质，定量评估了膨胀介质与静态等效介质间标度律的准确性，发现采用温度幂律衰减的膨胀介质可显著改善结果，为现实演化介质中的能量损失研究奠定基础。
We investigate the possible thermalization process of the highly occupied and weakly coupled Yang-Mills fields expanding along the beam axis through an evaluation of the entropy, particle number, and pressure anisotropy. The time evolution of the system is calculated by solving the equation of motion for the Wigner function in the semiclassical approximation with initial conditions mimicking the glasma. For the evaluation of the entropy, we adopt the Husimi-Wehrl (HW) entropy, which is obtained by using the Husimi function, a positive semidefinite quantum distribution function given by smearin…
We report recent results on the role of instabilities in the isotropization and thermalization of a longitudinally expanding system of quantum fields.
We found the deviation of the equation of state from ultrarelativistic one due to quantum corrections for a nonequilibrium longitudinally expanding scalar field. Relaxation of highly excited quantum field is usually described in terms of Classical Statistical Approximation (CSA). However, the expansion of the system reduces the applicability of such a semiclassical approach as the CSA making quantum corrections important. We calculate the evolution of the trace of the energy-momentum tensor within the Keldysh-Schwinger framework for static and longitudinal expanding geometries. We provide anal…
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 quar…
Particle production by expanding in the future light cone scalar quantum field is studied by assuming that the initial state is associated with the quasiequilibrium statistical operator corresponding to fluid dynamics. We calculate particle production from a longitudinally boost-invariant expanding quantum field designed as a simple but reliable model for the central rapidity region of a relativistic collision. Exact diagonalization of the model is performed by introducing a notion of quasiparticles.
We argue that the two-particle momentum correlation functions of high-multiplicity $p+p$ collisions at the LHC provide a signal for a ground state structure of a quasi equilibrium state of the longitudinally boost-invariant expanding quantum field which lies in the future light cone of a collision. The physical picture is that pions are produced by the expanding quantum emitter with two different scales approximately attributed to the expanding ideal gas in local equilibrium state and ground-state condensate. Specifically, we show that the effect of suppressing the two-particle Bose-Einstein m…
Adiabatic hydrodynamization and quasinormal modes of nonthermal attractors
本文通过绝热流体化框架，建立了非热吸引子的准正常模式与特征模式之间的对应关系，并推导出强纵向扩展系统的解析解。
A new method for evaluating spectra and correlations in the hydrodynamic approach is proposed. It is based on an analysis of Boltzmann equations (BE) in terms of probabilities for constituent particles to escape from the interacting system. The conditions of applicability of Cooper-Frye freeze-out prescription are considered within the method. The results are illustrated with a non-relativistic exact solution of BE for expanding spherical fireball as well as with approximate solutions for ellipsoidally expanding ones.
Evolution of spatially anisotropic perturbation created in the system formed after Relativistic Heavy Ion Collisions has been studied. The microscopic evolution of the fluctuations has been examined within the ambit of Boltzmann Transport Equation (BTE) in a hydrodynamically expanding background. The expansion of the background composed of Quark Gluon Plasma (QGP) is treated within the framework of relativistic hydrodynamics. Spatial anisotropic fluctuations with different geometry have been evolved through Boltzmann equation. It is observed that the trace of such fluctuation survive the evolu…
We investigate the far-from-equilibrium behavior of the Boltzmann equation for a gas of massless scalar field particles with quartic (tree level) self-interactions ($λϕ^4$) in Friedmann-Lemaitre-Robertson-Walker spacetime. Using a new covariant generating function for the moments of the Boltzmann distribution function, we analytically determine a subset of the spectrum and the corresponding eigenfunctions of the linearized Boltzmann collision operator. We show how the covariant generating function can be also used to find the exact equations for the moments in the full nonlinear regime. Differ…
We discuss the role of elastic and inelastic collisions and their interplay in the thermalization of the quark-gluon plasma. We consider a simplified situation of a static plasma, spatially uniform and isotropic in momentum space. We focus on the small momentum region, which equilibrates first, and on a short time scale. We obtain a simple kinetic equation that allows for an analytic description of the most important regimes. The present analysis suggests that the formation of a Bose condensate, expected when only elastic collisions are present, is strongly hindered by the inelastic, radiative…
Quantum kinetic approach to the Schwinger production of scalar particles in an expanding universe
本文在膨胀宇宙背景下，基于WKB解和Bogolyubov系数推导出描述Schwinger对产生的量子Vlasov方程组，该方程组具有大动量快速衰减和尊重共形对称性两个优点，并给出了紫外发散的抵消方案。
We study (3+1)D kinetic (Boltzmann-Vlasov) equations for relativistic plasma particles in a one-dimensionally expanding geometry motivated by ultrarelativistic heavy-ion collisions. We set up local equations in terms of Yang-Mills potentials and auxiliary fields that allow simulations of hard-(expanding)-loop (HEL) dynamics on a lattice. We determine numerically the evolution of plasma instabilities in the linear (Abelian) regime and also derive their late-time behavior analytically, which is consistent with recent numerical results on the evolution of the so-called melting color-glass condens…
We investigate the impact of hydrodynamic fluctuations on correlation functions in a scale invariant fluid with a conserved $U(1)$ charge. The kinetic equations for the two-point functions of pressure, momentum and heat energy densities are derived within the framework of stochastic hydrodynamics. The leading non-analytic contributions to the energy-momentum tensor as well as the $U(1)$ current are determined from the solutions to these kinetic equations. In the case of a static homogeneous background we show that the long time tails obtained from hydro-kinetic equations reproduce the one-loop…
We obtain an exact correspondence between the dynamical equations in Israel-Stewart (IS) theory and first-order causal and stable (FOCS) hydrodynamics for a boost-invariant system with an ideal gas equation of state at finite baryon chemical potential. Explicit expressions for the temperature and chemical potential dependence of the regulators in the FOCS theory are given in terms of the kinetic coefficients and constant relaxation time of the IS theory. Using the correspondence between the IS and FOCS theory, stability conditions for a charged fluid which are known in the FOCS approach are ap…
We study the far-off-equilibrium dynamics of a Bjorken expanding non-conformal system within kinetic theory and hydrodynamics. We show that, in contrast to the conformal case, neither shear nor bulk viscous pressure relax quickly to a non-equilibrium attractor. In kinetic theory an early-time, far-from-equilibrium attractor exists for the scaled longitudinal pressure, driven by the rapid longitudinal expansion of the medium. Second-order dissipative hydrodynamics fails to accurately describe this attractor, but a modified anisotropic hydrodynamic formulation reproduces it and provides excellen…
The plasma of quarks and gluons created in ultrarelativistic heavy-ion collisions turns out to be paramagnetic. In the presence of a background magnetic field, this paramagnetism thus leads to a pressure anisotropy, similar to anisotropies appearing in a viscous fluid. In the present paper, we use this analogy, and develop a framework similar to anisotropic hydrodynamics, to take the pressure anisotropy caused, in particular, by the nonvanishing magnetization of a plasma of quarks and gluons into account. We consider the first two moments of the classical Boltzmann equation in the presence of …
The temperature dependence of the kinetic coefficients is obtained in the non-perturbative region with the help of Green-Kubo-type formulae in the model of massive gluon gas motivated by numerical results from simulations of lattice QCD. The entropy production rate is estimated using scaling hydrodynamics. It is shown that the increase in the viscosity coefficients leads to entropy generation in heavy ion collision processes which could be big, especially for temperatures close to the critical one.
I set out the 2PI formalism for quantum fields in a Friedmann-Robertson-Walker Universe. I show how one can solve self-consistently for the quantum field evolution and the evolution of the cosmological scale factor, using a renormalised semi-classical Friedmann equation. In a 2PI coupling expansion truncated at O(lambda^2), I perform sample calculations demonstrating kinetic and chemical equilibration in this context.
We investigate entropy production for an expanding system of particles and resonances with isospin symmetry -- in our case pions and $ρ$ mesons -- within the framework of relativistic kinetic theory. A cascade code to simulate the kinetic equations is developed and results for entropy production and particle spectra are presented.
We obtain non-linear kinetic equations for sterile neutrino occupancies and lepton minus baryon numbers by matching real time correlation functions of thermal fluctuations computed in an effective description to those computed in thermal quantum field theory. After expanding in the sterile-neutrino Yukawa couplings, the coefficients in the equations are written as real time correlation functions of Standard Model operators. Our kinetic equations are valid for an arbitrary number of sterile neutrinos of any mass spectrum. They can be used to describe, e.g., low-scale leptogenesis via neutrino o…
By decomposing the distribution functions and color field to regular and fluctuation parts, the solution of the semi-classical kinetic equations of quark-gluon plasma is analyzed. Through expanding the kinetic equations of the fluctuation parts to third order, the nonlinear permittivity including the self-interaction of gauge field is obtained and a rough numerical estimate is given out for the important $\vk =0$ modes of the pure gluon plasma.
The cosmological perturbations on a bouncing brane are studied. The brane is moving inside a Klebanov-Strassler throat where the infra-red region of the geometry is smoothly cut off. For an observer confined to the world-volume of the brane, this results in a non-singular bouncing mirage cosmology. We have calculated the scalar perturbations corresponding to the normal displacements of the brane. This is performed in the probe brane limit where the gravitational back-reaction of the brane on the bulk throat is absent. Our model provides a framework for studying the transfer of fluctuations fro…
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