Xin An
We review the recent development on a systematic deterministic formalism describing dynamics of both bulk and fluctuations in an arbitrary relativistic hydrodynamic flow carrying conserved charges. In particular, we discuss the implementation of such general formalism near the QCD critical point.
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Relativistic fluctuations in stochastic fluid dynamics
本文围绕相对论流体中的非高斯涨落动力学，介绍并讨论了一种协变描述的最新理论形式体系。
For the understanding of fluctuation measurements in heavy-ion collisions it is crucial to develop quantitatively reliable dynamical descriptions which take the non-perturbative nature of QCD near the phase transition into account. We discuss a novel QCD-assisted transport approach based on non-equilibrium chiral fluid dynamics and the effective action of low energy QCD. In this framework, we study the time-evolution of fluctuation measures of the critical mode, notably the kurtosis, for a non-expanding system. From this, we can estimate the equilibration times of critical mode fluctuations in…
To describe dynamics of bulk and fluctuations near the QCD critical point we develop general relativistic fluctuation formalism for a fluid carrying baryon charge. Feedback of fluctuations modifies hydrodynamic coefficients including bulk viscosity and conductivity and introduces nonlocal and non-instantaneous terms in constitutive equations. We perform necessary ultraviolet (short-distance) renormalization to obtain cutoff independent deterministic equations suitable for numerical implementation. We use the equations to calculate the universal non-analytic small-frequency dependence of transp…
The proper-time 4d path integral is used as a starting point to derive the new explicit parametric form of the quark-antiquark Green's function in gluonic and QED fields, entering as a common Wilson loop. The subsequent vacuum averaging of the latter allows to derive the instantaneous Hamiltonian. The explicit form and solutions are given in the case of the $q\bar q$ mesons in magnetic field.
In this contribution the role of quantum fluctuations for the QCD phase diagram is discussed. This concerns in particular the importance of the matter back-reaction to the gluonic sector. The impact of these fluctuations on the location of the confinement/deconfinement and the chiral transition lines as well as their interrelation are investigated. Consequences of our findings for the size of a possible quarkyonic phase and location of a critical endpoint in the phase diagram are drawn.
We investigate the behaviour of the QCD evolution towards high-energy, in the diffusive approximation, in the limit where the fluctuation contribution is large. Our solution for the equivalent stochastic Fisher equation predicts the amplitude as well as the whole set of correlators in the strong noise limit. The speed of the front and the diffusion coefficient are obtained. We analyse the consequences on high-energy evolution in QCD.
We present an attempt towards constructing relativistic quark-gluon quasi-potentials from QCD using Unitary Clothing Transformations (UCT) approach. The brief review of the UCT method is given. Starting from a simplified model of QCD hamiltonian (H), we define the 'color-clothed' representation (CCR) of H. In this representaion, it is required that only color-singlet states are the eigenstates of the H. In CCR, H contains the family of quantum relativistic potentials acting between 'color clothed' quarks and gluons. Simultaneously, newly defined quarks acquire new masses (expected to be close …
Stochastic fluctuations in relativistic fluids: causality, stability, and the information current
本研究建立了纳入因果性与稳定性最新进展的相对论流体平衡态随机涨落通用形式体系，适用于各类协变稳定黏性流体理论，并通过热扩散模型、共形不变Israel-Stewart理论验证其有效性，还探究了两点函数的框架依赖性。
We derive a formula that defines quantum fluctuations of energy in subsystems of a hot relativistic gas. For small subsystem sizes we find substantial increase of fluctuations compared to those known from standard thermodynamic considerations. However, if the size of the subsystem is sufficiently large, we reproduce the result for energy fluctuations in the canonical ensemble. Our results are subsequently used in the context of relativistic heavy-ion collisions to introduce limitations of the concepts such as classical energy density or fluid element. In the straightforward way, our formula ca…
The low-energy sector of QCD with $N_f = 2\!+\!1$ dynamical quark flavors at non-vanishing chemical potential and temperature is studied with a non-perturbative functional renormalization group method. The analysis is performed in different truncations in order to explore fluctuation-induced modifications of the quark-meson correlations as well as quark and meson propagators on the chiral phase transition of QCD. Depending on the chosen truncation significant quantitative implications on the phase transition are found. In the chirally symmetric phase, the quark flavor composition of the pseudo…
Non-Gaussian fluctuations in relativistic hydrodynamics: Confluent equations for three-point correlations
本文推导了相对论随机流体动力学中非高斯波动演化的确定性方程，通过定义平均局部Landau框架及波动流体动力学变量，提出统一的多组分矩阵形式，引入新的相对论形式，实现局部空间基底SO(3)旋转的协变性。
Quantum features of the baryon number fluctuations in subsystems of a hot and dense relativistic gas of fermions are analyzed. We find that the fluctuations in small systems are significantly increased compared to their values known from the statistical physics, and diverge in the limit where the system size goes to zero. The numerical results obtained for a broad range of the thermodynamic parameters expected in heavy-ion collisions are presented. They can be helpful to interpret and shed new light on the experimental data.
We study the effect of quantum and thermal fluctuations as well as the mass dependence of the phase structure of QCD at finite temperature and density within a dynamical Polyakov-loop--extended quark-meson model. The glue dynamics is simulated by the Polyakov-loop potential, also including the back-coupling of the matter sector to the glue dynamics. In the chiral limit, the chiral phase transition at large chemical potential and low temperature splits into two transition branches. For non-vanishing pion masses the chiral transition at small chemical potential changes from a phase transition to…
The holographic mapping of gravity in AdS space to QCD, quantized at fixed light-front time, provides a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. In particular, the elastic and transition form factors of the pion and the nucleons are well described in this framework. The light-front AdS/QCD holographic approach thus gives a frame-independent first approximation of the color-confining dynamics, spectroscopy, and excitation spectra o…
The low-lying eigenmodes of the Dirac operator associated with typical gauge field configurations in QCD encode, among other low-energy properties, the physics behind the solution to the $U_A(1)$ problem (i.e. the origin of the $η'$ mass), the nature of spontaneous chiral symmetry breaking, and the physics of string-breaking, quark-antiquark pair production, and the OZI rule. Moreover, the space-time chiral structure of these eigenmodes reflects the space-time topological structure of the underlying gauge field. We present evidence from lattice QCD on the local chiral structure of low Dirac ei…
Recent developments in relativistic hydrodynamic fluctuations
本文从随机流体力学、流体动理学和有效场论三个互补框架综述相对论性流体力学热涨落的最新理论进展，并比较其异同与贡献。
The purpose of this paper is twofold. Firstly, we study the dynamical density fluctuations around the critical point(CP) of Quantum Chromodynamics(QCD) using dissipative relativistic fluid dynamics in which the coupling of the density fluctuations to those of other conserved quantities is taken into account. We show that the sound mode which is directly coupled to the mechanical density fluctuation is attenuated and in turn the thermal mode becomes the genuine soft mode at the QCD CP. We give a speculation on the possible fate of a Mach cone in the vicinity of the QCD CP as a signal of the exi…
We report the continuum limits of the speed of sound, c_s, and the specific heat at constant volume, c_v, in quenched QCD at temperatures of 2Tc and 3Tc. At these temperatures, c_s is within 2-sigma of the ideal gas value, whereas c_v differs significantly from the ideal gas. However, both are compatible with results expected in a theory with conformal symmetry. We investigate effective measures of conformal symmetry in the high temperature phase of QCD.
First we review the derivation of the relativistic flux tube model for a quark-antiquark system from Wilson area law as we have given in a preceding paper. Then we extend the method to the three-quark case and obtain a Lagrangian corresponding to a star flux tube configuration. A Hamiltonian can be explicitly constructed as an expansion in $1 / m^2$ or in the string tension $σ$. In the first case it reproduces the Wilson loop three-quark semirelativistic potential; in the second one, very complicated in general, but it reproduces known string models for slowly rotating quarks.
The magnitude of the strong interaction is characterized by $α_s$, the coupling parameter in Quantum Chromodynamics (QCD), a parameter with an unexplained value in the Standard Model. In this paper, a candidate explanation for $α_s$ is derived from (1) the lifetime of quark-antiquark pairs in vacuum fluctuations given by the Uncertainty Principle, (2) the variation of $α_s$ as a function of energy in QCD, and (3) classical relativistic dynamics of the quarks and antiquarks. A semiclassical model for heavy quark-antiquark vacuum fluctuations is described herein, based on (2) and (3). The model …
We study the local violation of P and CP invariance in heavy ion collisions as observed at RHIC and LHC using a simple "deformed QCD" model. This model is a weakly coupled gauge theory, which however has all the relevant crucial elements allowing us to study difficult and nontrivial questions which are known to be present in real strongly coupled QCD. Essentially, we want to understand the physics of long range order in form of coherent low dimensional vacuum configurations observed in Monte Carlo lattice simulations. Apparently precisely such kind of configurations are responsible for suffici…
The non-Gaussian fluctuations of baryon density are sensitive to the presence of the conjectured QCD critical point. Their observational consequences are crucial for the ongoing experimental search for this critical point through the beam energy scan program at Relativistic Heavy Ion Collider (RHIC). In the expanding fireball created in a heavy-ion collision, critical fluctuations would inescapably fall out of equilibrium, and require a systematic description within a dynamical framework. In this paper, we employ newly developed effective field theory (EFT) for fluctuating hydrodynamics to stu…
We show how, contrary to physical intuition, thermal fluctuations of physical states having a non-vanishing baryonic number can be fully neglected in the thermodynamics of QCD at any physical temperature. We also discuss on the consistency between our results and the CPT theorem. The last part of this article is devoted to comment some interesting physical features which follow from this result.
These are pedagogical lecture notes on hydrodynamic fluctuations in normal relativistic fluids. The lectures discuss correlation functions of conserved densities in thermal equilibrium, interactions of the hydrodynamic modes, an effective action for viscous fluids, and the breakdown of the derivative expansion in hydrodynamics.
A QCD inspired relativistic effective Hamiltonian model for the bound states of mesons has been constructed, which integrates the advantages of several QCD effective Hamiltonian models. Based on light-front QCD effective Hamiltonian model, the squared invariant mass operator of meson is used as the effective Hamiltonian. The model has been improved significantly in four major aspects: i)it is proved that in center of mass frame and in internal coordinate Hilbert subspace, the total angular momentum $J$ of meson is conserved and the mass eigen equation can be expressed in total angular momentum…
A rigorous three-dimensional relativistic equation for quark-antiquark bound states at finite temperature is derived from the thermal QCD generating functional which is formulated in the coherent-state representation. The generating functional is derived newly and given a correct path-integral expression. The perturbative expansion of the generating functional is specifically given by means of the stationary-phase method. Especially, the interaction kernel in the three-dimensional equation is derived by virtue of the equations of motion satisfied by some quark-antiquark Green functions and giv…
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