Momentum-dependent flow fluctuations as a hydrodynamic response to initial geometry
Maurício Hippert, David Dobrigkeit Chinellato, Matthew Luzum, Jorge Noronha, Tiago Nunes da Silva, Jun Takahashi
备注：
4 pages, 2 figures, contribution to the proceedings of XXVIIIth International Conference on Ultrarelativistic Nucleus-Nucleus Collisions (Quark Matter 2019)
We propose a redefinition of the principal component analysis (PCA) of anisotropic flow that makes it more directly connected to fluctuations of the initial geometry of the system. Then, using state-of-the-art hydrodynamic simulations, we make an explicit connection between flow fluctuations and a cumulant expansion of the initial transverse geometry. In particular, we show that the second principal component of elliptic flow is generated by higher-order cumulants, and therefore probes smaller length scales of the initial state. With this information, it will be possible to put new constraints on properties of the early-time dynamics of a heavy-ion collision, including small-scale structure, as well as properties of the quark-gluon plasma.
This proceeding briefly summarizes our recent work on calculating the correlated fluctuations of net protons on the hydrodynamic freeze-out surface near the QCD critical point. For both Poisson and Binomial baselines, our calculations could roughly reproduce the energy dependent cumulant $C_4$ and $κσ^2$ of net protons, but always over-predict $C_2$ and $C_3$ due to the positive contributions from the static critical fluctuations.
We develop a new integrated dynamical model to investigate the effects of the hydrodynamic fluctuations on observables in high-energy nuclear collisions. We implement hydrodynamic fluctuations in a fully 3-D dynamical model consisting of the hydrodynamic initialization models of the Monte-Carlo Kharzeev-Levin-Nardi model, causal dissipative hydrodynamics and the subsequent hadronic cascades. By analyzing the hadron distributions obtained by massive event-by-event simulations with both of hydrodynamic fluctuations and initial-state fluctuations, we discuss the effects of hydrodynamic fluctuatio…
We present a novel approach to the treatment of thermal fluctuations in the (3+1)-D viscous hydrodynamic simulation MUSIC. The phenomenological impact of thermal fluctuations on hadronic observables is investigated using the IP-Glasma + hydrodynamics + hadronic cascade hybrid approach. The anisotropic flow observed in heavy-ion collision experiments is mostly attributed to the hydrodynamic response to the event-by-event collision geometry and to the sub-nucleon quantum fluctuations. However, hydrodynamic fluctuations are present during the dynamical evolution of the Quark Gluon Plasma (QGP) an…
To integrate hydrodynamic fluctuations, namely thermal fluctuations of hydrodynamics, into dynamical models of high-energy nuclear collisions based on relativistic hydrodynamics, the property of the hydrodynamic fluctuations given by the fluctuation-dissipation relation should be carefully investigated. The fluctuation-dissipation relation for causal dissipative hydrodynamics with the finite relaxation time is naturally given in the integral form of the constitutive equation by the linear-response theory. While, the differential form of the constitutive equation is commonly used in analytic in…
Rapidity decorrelation in high energy heavy-ion collisions is one of the hot topics in understanding longitudinal dynamics of the quark gluon plasma (QGP). In this study we employ an integrated dynamical model with full three dimensional relativistic hydrodynamics and perform event-by-event numerical simulations of Pb+Pb collisions at the LHC energy. We analyze factorization ratios to understand rapidity decorrelation from hydrodynamic fluctuations and initial longitudinal fluctuations. We show that factorization breaking happens due to both hydrodynamic fluctuations and initial longitudinal f…
We investigate the effect of hydrodynamic fluctuations on the rapidity decorrelations of anisotropic flow in high-energy nuclear collisions using a (3+1)-dimensional integrated dynamical model. The integrated dynamical model consists of twisted initial conditions, fluctuating hydrodynamics, and hadronic cascades on an event-by-event basis. To understand the rapidity decorrelation, we analyze the factorization ratio in the longitudinal direction. Comparing the factorization ratios between fluctuating hydrodynamics and ordinary viscous hydrodynamics, we find a sizable effect of hydrodynamic fluc…
We discuss rapidity decorrelation caused by hydrodynamic fluctuations in high-energy nuclear collisions at the LHC energy. We employ an integrated dynamical model which is a combination of the Monte Carlo version of Glauber model with extension to longitudinal direction for initial conditions, full three-dimensional relativistic fluctuating hydrodynamics for the space-time evolution of created matter in the intermediate stage and a hadronic cascade model in the late stage. We switch on and off the hydrodynamic fluctuations in the hydrodynamic stage to understand the effects of hydrodynamic flu…
We develop a set of kinetic equations for hydrodynamic fluctuations which are equivalent to nonlinear hydrodynamics with noise. The hydro-kinetic equations can be coupled to existing second order hydrodynamic codes to incorporate the physics of these fluctuations, which become dominant near the critical point. We use the hydro-kinetic equations to calculate the modifications of energy momentum tensor by thermal fluctuations from the earliest moments and at late times in Bjorken expansion. The solution to the kinetic equations precisely determines the coefficient of the first fractional power (…
I present an overview of recent theoretical results on fluctuations of conserved charges in heavy-ion collisions obtained in relativistic hydrodynamics and molecular dynamics frameworks. In particular, I discuss the constraints on the location of the QCD critical point based on comparisons of experimental data on proton number cumulants with precision calculations of non-critical contributions. Recent developments on critical fluctuations in molecular dynamics simulations are covered as well.
We investigate effects of causal hydrodynamic fluctuations in the longitudinally expanding quark gluon plasma on final entropy distributions in high-energy nuclear collisions.
We investigate the interplay between hydrodynamic fluctuations and initial longitudinal fluctuations for their effects on the rapidity decorrelation of collective flow in high-energy nuclear collisions. We use a (3+1)-dimensional integrated dynamical model in which we combine initial conditions with longitudinal fluctuations, fluctuating hydrodynamics and hadronic cascades. We analyse the factorisation ratio in the longitudinal direction to study the effect of these fluctuations on the rapidity decorrelation. We find an essential difference between the effects of the hydrodynamic fluctuations …
The field of high energy nuclear collisions has witnessed a surge of interest in the role played by hydrodynamic fluctuations. Hydrodynamic fluctuations may have significant effects on matter created in heavy-ion accelerators whose trajectories in the plane of temperature versus chemical potential pass near a possible critical endpoint. We extend previous studies to explore the impact of these fluctuations on Hanbury Brown-Twiss interferometry of identical hadrons. With an appropriately defined correlation function we find that the fluctuations increase substantially when the trajectory passes…
We carry out a principal component analysis of fluctuations in a hydrodynamic simulation of heavy-ion collisions, and compare with experimental data from the CMS collaboration. The leading and subleading principal components of elliptic and triangular flow reproduce the trends seen in data. By contrast, the principal components of multiplicity fluctuations show an interesting difference in their $p_T$ dependence for simulations compared to experimental data. Specifically, the leading component increases with $p_T$ in hydrodynamics, while it is constant in experiment. In order to understand how…
The fluctuation-dissipation relation tells that dissipation always accompanies with thermal fluctuations. Relativistic fluctuating hydrodynamics is used to study the effects of the thermal fluctuations in the hydrodynamic expansion of the quark-gluon plasma created in the high-energy nuclear collisions. We show that the thermal noise obeys the steady-state fluctuation theorem when (i) the time scales of the evolution of thermodynamic quantities are sufficiently longer than the relaxation time, and (ii) the thermal fluctuations of temperature are sufficiently small. The steady-state fluctuation…
We develop a set of kinetic equations for hydrodynamic fluctuations which are equivalent to nonlinear hydrodynamics with noise. The hydro-kinetic equations can be coupled to existing second order hydrodynamic codes to incorporate the physics of these fluctuations. We first show that the kinetic response precisely reproduces the renormalization of the shear viscosity and the fractional power ($\propto ω^{3/2}$) which characterizes equilibrium correlators of energy and momentum for a static fluid. Then we use the hydro-kinetic equations to analyze thermal fluctuations for a Bjorken expansion, ev…
The amount of axial charge produced in heavy ion collisions is one of the key quantities in understanding chiral magnetic effect. Current phenomenological studies assume large axial charge chemical potential $μ_5$ produced in Glasma phase and assume the conservation of axial charge throughout the evolution, which is valid in the long relaxation time limit. Based on the solution of stochastic hydrodynamics with phenomenological parameters, our study suggests that the situation of heavy ion collisions may be close to the opposite limit, in which axial charge fluctuation approaches thermodynamic …
Hydrodynamics is a general theoretical framework for describing the long-time large-distance behaviors of various macroscopic physical systems, with its equations based on conservation laws such as energy-momentum conservation and charge conservation. Recently there has been significant interest in understanding the implications of angular momentum conservation for a corresponding hydrodynamic theory. In this work, we examine the key conceptual issues for such a theory in the relativistic regime where the orbital and spin components get entangled. We derive the equations for relativistic visco…
Effects of initial flow velocity fluctuation in event-by-event (3+1)D hydrodynamics
在（3+1）D理想流体力学模型中，采用AMPT Monte Carlo模型给出的涨落初始条件，研究了高能重离子碰撞中的强子谱和椭圆流.在RHIC和LHC的能量从事件的模拟结果与实验数据进行了比较。初始能量密度的涨落不仅来自于重叠核子的相干软相互作用的数目，而且还来自于每次二元核子碰撞中的非相干半硬部分子散射。半硬部分子散射的微喷流被假定为局部热化通过高斯涂抹，并引起非零的初始局部流速。由于初始径向流速的非零性，初始流速的涨落导致末态强子的横动量谱更硬。在快度分布的初始波动导致扩大热点在纵向方向上，并示出在大的横向动量，导致一个相当大的减少最终强子椭圆流。
Characterization of initial fluctuations for the hydrodynamical description of heavy ion collisions
逐事件波动的初始条件的流体动力学描述的重离子碰撞的特点。我们提出了一个贝塞尔-傅立叶分解的方位角，在横向平面的半径和快度。这允许在所有流体动力学领域的波动，包括能量密度，压力，流体速度，剪切应力和体积粘性压力的完整表征。它的优点是波动可以相对于它们的波长进行排序，并且它们可以在流体动力学形式体系内逐模式传播。然后，事件集合可以根据函数概率分布来表征。对于Monte Carlo Glauber模型的事件系综，我们提供的证据表明，后者接近高斯形式，从而允许一个特别简单的事件分布的表征。
We analyze the combined effects of hydrodynamic fluctuations and chiral magnetic effect (CME) for a chiral medium in the presence of a background magnetic field. Based on the recently developed non-equilibrium effective field theory, we show fluctuations give rise to a CME-related positive contribution to magnetoresistance, while the early studies without accounting for the fluctuations find a CME-related negative magnetoresistance. At zero axial relaxation rate, the fluctuations contribute to the transverse conductivity in addition to the longitudinal one.
Multiplicity fluctuations are one of the most crucial observables in the Beam Energy Scan program of the Relativistic Heavy Ion Collider. It is understood that they can be utilized to probe the whereabouts of the critical point on the phase diagram of the QCD matter. However, a significant portion of these fluctuations is, apart from that related to the QCD phase transition, attributed to the other origins, which we refer to as "noncritical" ones. The present study is dedicated to the noncritical aspects of the multiplicity fluctuations in heavy-ion collisions. In particular, we focus on those…
A key ingredient of hydrodynamical modeling of relativistic heavy ion collisions is thermal initial conditions, an input that is the consequence of a pre-thermal dynamics which is not completely understood yet. In the paper we employ a recently developed energy-momentum transport model of the pre-thermal stage to study influence of the alternative initial states in nucleus-nucleus collisions on flow and energy density distributions of the matter at the starting time of hydrodynamics. In particular, the dependence of the results on isotropic and anisotropic initial states is analyzed. It is fou…
Charge fluctuations for a baryon-neutral quark-gluon plasma have been calculated in lattice gauge theory. These fluctuations provide a well-posed rigorous representation of the quark chemistry of the vacuum for temperatures above T_c >~ 155 MeV. Due to the finite lifetime and spatial extent of the fireball created in relativistic heavy ion collisions, charge-charge correlations can only equilibrate for small volumes due to the finite time required to transport charge. This constraint leads to charge correlations at finite relative position that evolve with time. The source and evolution of suc…
In this article a correspondence has been established between the out of equilibrium system dissipation and the thermodynamic field redefinition of the macroscopic variables through the momentum dependent relaxation time approximation (MDRTA) solution of relativistic transport equation. Here, it has been shown that the out of equilibrium thermodynamic fields are not uniquely defined and are subjected to include dissipative effects from the medium. A second order relativistic hydrodynamic theory has been developed including such dissipative effects. The necessary conditions for developing a hyd…
Critical net-proton number fluctuations with hydrodynamics
Dalian University of Technology（大连理工大学）；Justus-Liebig-Universität Gießen（吉森大学）；University of California, Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Central China Normal University（华中师范大学）
We predict that the mean transverse momentum of charged hadrons $\langle p_t\rangle$ rises as a function of the charged-particle multiplicity in ultracentral nucleus-nucleus collisions. We explain that this phenomenon has a simple physical origin and represents an unambiguous prediction of the hydrodynamic framework of heavy-ion collisions. We argue that the relative increase of $\langle p_t \rangle$ is proportional to the speed of sound squared $c_s^2$ of the quark-gluon plasma. Based on the value of $c_s^2$ from lattice QCD, we expect $\langle p_t\rangle$ to increase by approximately $18$ Me…
The search for the QCD critical point in heavy-ion collision experiments requires dynamical simulations of the bulk evolution of QCD matter as well as of fluctuations. We consider two essential ingredients of such a simulation: a generic extension of hydrodynamics by a_parametrically_ slow mode or modes ("Hydro+") and a description of fluctuations out of equilibrium. By combining the two ingredients we are able to describe the bulk evolution and the fluctutations within the same framework. Critical slowing down means that equilibration of fluctuations could be as slow as hydrodynamic evolution…
A second order relativistic hydrodynamic theory has been derived using momentum dependent relaxation time in the relativistic transport equation. In order to do that, an iterative technique of gradient expansion approach, namely Chapman-Enskog (CE) expansion of the particle distribution function has been employed. The key findings of this work are, (i) momentum dependent relaxation time in collision term results in an extended Landau matching condition for the thermodynamic variables, (ii) the result from numerical solution of Boltzmann equation lies somewhere in between the two popular extrem…
Hydro-kinetic theory of thermal fluctuations is applied to a non-conformal relativistic fluid. Solving the hydro-kinetic equations for an isotropically expanding background we find that hydrodynamic fluctuations give ultraviolet divergent contributions to the energy-momentum tensor. After shifting the temperature to account for the energy of non-equilibrium modes, the remaining divergences are renormalized into local parameters, e.g. pressure and bulk viscosity. We also confirm that the renormalization of the pressure and bulk viscosity is universal by computing them for a Bjorken expansion. T…
A newly proposed framework of perfect-fluid relativistic hydrodynamics for particles with spin 1/2 is briefly reviewed. The hydrodynamic equations follow entirely from the conservation laws for energy, momentum, and angular momentum. The incorporation of the angular-momentum conservation requires that the spin polarization tensor is introduced. It plays a role of a Lagrange multiplier conjugated to the spin tensor. The space-time evolution of the spin polarization tensor depends on the specific form chosen for the spin tensor.
In event by event hydrodynamic model, we have simulated 30-40\% Au+Au collisions at RHIC and computed the slope parameter from the invariant pion distribution. In each event, the slope parameter fluctuates azimuthally. Fourier expansion coefficients $T_n$ for the slope parameter and the Fourier expansion coefficients $v_n$ for the azimuthal distribution $\frac{dN}{dϕ}$ are found to be strongly correlated. Strong correlation between the two expansion coefficients suggests that in addition to azimuthal distribution, fluctuations in the slope parameter of the invariant distribution can as well be…
Effect of longitudinal fluctuation in event-by-event (3+1)D hydrodynamics
采用AMPT Monte Carlo模型，在波动初始条件下，采用逐事件（3+1）D理想流体动力学模拟方法研究了相对论性重离子碰撞中的强子谱和椭圆流.研究了受伤核子的相干软胶子产生和半硬部分子散射中的非相干微喷注产生。这些部分子参与部分子级联，并被假定为局部热化的。它们为具有高斯拖尾的流体动力学模拟提供了波动的初始条件。研究了横向和纵向波动的影响。沿快度方向的初始扰动导致热点沿纵向扩展，这将降低椭圆流和高横动量粒子的产额。在涨落初始条件中引入的内禀关联也影响末态强子的双强子关联。
Shear viscosity from fluctuations in linearized relativistic hydrodynamics
České vysoké učení technické v Praze（布拉格捷克理工大学）；SUBATECH UMR 6457 (IMT Atlantique, Université de Nantes, IN2P3/CNRS)（南特大学/大西洋高等理工学院/法国国家科学研究中心）；Univerzita Mateja Bela（马特伊·贝尔大学）
