David Blaschke, Gerd Röpke, Dmitry N. Voskresensky, Vladimir G. Morozov
We discuss how the nonequilibrium process of pion production within the Zubarev approach of the nonequilibrium statistical operator leads to a theoretical foundation for the appearance of a nonequilibrium pion chemical potential for the pion distribution function for which there is experimental evidence in experiments at the CERN LHC.
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Generalized relativistic second order magnetohydrodynamics: A correlation function approach using Zubarev's nonequilibrium statistical operator
本文基于总能量动量守恒和Bianchi恒等式，构建了Zubarev非平衡统计算符框架下的相对论第二阶磁流体力学，推导了所有耗散张量，并给出了第二阶输运系数的Kubo公式。
Second-order spin hydrodynamics from Zubarev's nonequilibrium statistical operator formalism
本文基于祖巴列夫非平衡统计算子形式推导相对论自旋流体动力学中耗散张量的二阶表达式，引入自旋密度为独立变量得到新输运系数，推导相关张量演化方程，完善自旋流体动力学理论。
Based on the Nakajima-Zubarev type nonequilibrium density operator, we derive a hyperbolic hydrodynamical equation. Microscopic Kubo-formulas for all coefficients in the hyperbolic hydrodynamics are obtained. Coefficients $α_{i}$'s and $β_{i}$'s in the Israel-Stewart equation are given as current-weighted correlation lengths which are to be calculated in statistical mechanics.
We extend chiral perturbation theory to study a meson gas out of thermal equilibrium. Assuming that the system is initially in equilibrium below the critical temperature and working within the Schwinger-Keldysh contour technique, we define consistently the time-dependent pion decay functions, the counterparts of the pion decay constants, and calculate them up to next to leading order. The link with curved space-time QFT allows to establish nonequilibrium renormalisation. The short-time behaviour and the applicability to a heavy-ion collision plasma are also discussed in this work.
We apply the formalism of Chiral Perturbation Theory out of thermal equilibrium to describe explosive production of pions via the parametric resonance mechanism. To lowest order the lagrangian is that of the Nonlinear Sigma Model where the pion decay constant becomes a time-dependent function. This model alows for a consistent nonequilibrium formulation within the framework of the closed time path method, where one-loop effects can be systematically accounted for and renormalized. We work in the narrow resonance regime where there is only one resonant band. The present approach is limited to r…
We develop a kinetic equation approach to nonequilibrium pion and sigma meson production in a time-dependent, chiral symmetry breaking field (inertial mechanism). We investigate the question to what extent the low-momentum pion enhancement observed in heavy-ion collisions at CERN - LHC can be addressed within this formalism. In a first step, we consider the inertial mechanism for nonequilibrium production of $σ-$mesons and their simultaneous decay into pion pairs for two cases of $σ$ mass evolution. The resulting pion distribution shows a strong low-momentum enhancement which can be approximat…
In a homogeneous pionic gas system, chemical nonequilibrium process is considered to understand its effect in the expansion processes that are realized immediately after heavy ion collisions. The chemical relaxation time is calculated by incorporating the $π+π\leftrightarrow π+π+π+π$ reaction, which is given in the second order of perturbation in the $σ$ model. The $π+π\leftrightarrow π+π+π+π$ reaction is assumed to be less frequent than the $π+π\leftrightarrow π+π$ scattering that is expected to establish the local equilibrium, and hydrodynamical equation is solved for various initial conditi…
We consider an interacting pion gas in the regime where thermal but not chemical equilibrium has been reached. Approximate particle number conservation is implemented by a nonvanishing pion chemical potential $μ_π$ within a diagrammatic thermal field theory approach, valid in principle for any bosonic field theory in this regime. The resulting Feynman rules are then applied within the context of Chiral Perturbation Theory to discuss thermodynamical quantities of interest for the pion gas such as the free energy, the quark condensate and thermal self-energy. In particular, we derive the $μ_π\ne…
Nonequilibrium Phenomenology of Identified Particle Spectra in Heavy-Ion Collisions at LHC Energies
本文通过非平衡统计算子方法研究重离子碰撞中低p_T区域的π谱增强现象，引入有效π化学势描述低能π态过载，并利用涨落波模型和粒子生成器分析ALICE实验数据，采用贝叶斯推断提取临界冻结超曲面的热力学参数。
We review our recent work on Chiral Lagrangians out of thermal equilibrium, which are introduced to analyse the pion gas formed after a Relativistic Heavy Ion Collision. Chiral Perturbation Theory is extended by letting $\fpi$ be time dependent and allows to describe explosive production of pions in parametric resonance. This mechanism could be relevant if hadronization occurs at the chiral phase transition.
We study static and dynamical critical phenomena of chiral symmetry breaking in a two-flavor Nambu--Jona-Lasinio constituent quark model. We obtain the low-energy effective action for scalar and pseudoscalar degrees of freedom to lowest order in quark loops and to quadratic order in the meson fluctuations around the mean field. The \emph{static} limit of critical phenomena is shown to be described by a Ginzburg-Landau effective action including \emph{spatial} gradients. Hence \emph{static} critical phenomena is described by the universality class of the O(4) Heisenberg ferromagnet. \emph{Dynam…
We explore the extension of chiral perturbation theory out of thermal equilibrium. The pion decay constant becomes then a time-dependent function and we work within the Schwinger-Keldysh contour technique. A useful connection with curved space-time QFT allows to renormalise the model. We discuss the applicability of our approach within a relativistic heavy-ion collision environment.
We discuss a dynamical mechanism of pion production from disoriented chiral condensates (DCC). It leads to an explosive production of pions via the parametric amplification mechanism, which is similar to the reheating mechanism in inflationary cosmology. Classically, it is related with the instability in the solutions of the Mathieu equation and we explore the quantum aspects of the mechanism. We show that nonlinearlities and back reactions can be ignorable for sufficiently long time under the small amplitude approximations of background $σ$ oscillations, which may be appropriate for the late …
The expansion and hadronization of a quark meson plasma is studied using an effective chiral interaction Lagrangian. The particles we consider are light as well as strange quarks, which can form pions, kaons and eta mesons via collision processes. The transport equations for the system are solved using a QMD type algorithm. We find that in chemical equilibrium at high temperatures the strange quark mass is considerably higher than the strange current quark mass and becomes even higher if we assume an initial state free of strange quarks. This leads to a considerably higher production threshold…
We discuss two-pion correlations as a possible experimental probe into disoriented chiral condensates. In particular, we point out that the iso-singlet squeezed states of the BCS type have peculiar two-particle correlations in the back-to-back and the identical momentum configurations which should be detectable experimentally. We motivate the examination of the squeezed state by showing that such state naturally appears in a final stage of nonequilibrium phase transitions via the parametric resonance mechanism proposed by Mrówczyński and Müller.
We investigate the problem of quantum back reactions due to particle production by the parametric resonance mechanism in an environment of nonequilibrium chiral phase transition. We work with the linear sigma model and employ Boyanovsky et al.'s formalism to take account of back reactions under the Hartree-Fock approximation. We calculate the single pion momentum distributions and two pion correlations under the initial condition of thermal equilibrium and small amplitude sigma oscillations around a potential minimum. We observe that the resonance peak survives under the back reaction which is…
We analyse the extension of Chiral Perturbation Theory to describe a meson gas out of thermal equilibrium. For that purpose, we let the pion decay constant be a time-dependent function and work within the Schwinger-Keldysh contour technique. A useful connection with curved space-time QFT allows to consistently renormalise the model, introducing two new low-energy constants in the chiral limit. We discuss the applicability of our approach within a Relativistic Heavy-Ion Collision environment. In particular, we investigate the formation of Disoriented Chiral Condensate domains in this model, via…
An appropriate statistical approach for nonequilibrium particle production
针对热模型无法重现K/π比值角状结构的问题，提出采用广义非广延统计方法，将其纳入强子共振气体模型，成功重现了非单调的K+/π+比值。
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