Transport coefficients of quark-gluon plasma

Transport coefficients of quark-gluon plasma are discussed in the framework of relativistic kinetic theory with the relaxation time approximation of Boltzmann transport equation. The expressions for the coefficients of shear and volume viscosities and heat conductivity are derived assuming quark-gluon plasma to be a non-reactive mixture of quarks, anti-quarks and gluons. A lowest order in deviations from local thermal equilibrium and in plasma phase, lowest order in coupling constant are assumed. Entropy production due to irreversible processes is discussed.     

The principle of corresponding states and the dynamic properties of simple liquids

We present a corresponding states analysis of existing data on sound velocity, transport coefficients and intermolecular interaction times of a number of simple fluids. With appropriate choices of parameters for the intermolecular pair potential, such properties as the adiabatic sound velocity, the shear and bulk viscosities, the thermal conductivity and the intermolecular interaction time can be reduced along the liquid-vapor equilibrium curve. Deviations from the simple law of corresponding states are most pronounced for the transport properties, indicating a stronger sensitivity of the dynamical properties to the interaction potential and the molecular structure.     

Transport coefficients of QCD matter

Transport coefficients of QCD matter are discussed in the framework of relativistic kinetic theory. Expressions for shear and bulk viscosities and heat conductivity are derived in lowest order in deviations from local thermal equilibrium. Pure gluon matter is considered both at low temperatures in the glueball phase and at high temperatures in the gluon plasma phase, and quark-gluon matter is considered in the high-temperature plasma phase. In the critical region nonperturbative calculations based on Kubo formulas should be attempted. Applications to ultra-relativistic nucleus-nucleus collisions are discussed.     

Transport coefficients near chiral phase transition

We analyze the transport properties of relativistic fluid composed of constituent quarks at finite temperature and density. We focus on the shear and bulk viscosities and study their behavior near chiral phase transition. We model the constituent quark interactions through the Nambu–Jona-Lasinio Lagrangian. The transport coefficients are calculated within kinetic theory under relaxation time approximation including in-medium modification of quasi-particles dispersion relations. We quantify the influence of the order of chiral phase transition and the critical end point on dissipative phenomena in such a medium.     

A kinetic theory of dense fluids

A new kinetic equation is developed which incorporates the desirable features of the Enskog, the Rice-Allnatt, and the Prigogine-Nicolis-Misguich kinetic theories of dense fluids. Advantages of the present theory over the latter three theories are (1) it yields the correct local equilibrium hydrodynamic equations, (2) unlike the Rice-Allnatt theory, it determines the singlet and doublet distribution functions from the same equation, and (3) unlike the Prigogine-Nicolis-Misguich theory, it predicts the kinetic and kinetic-potential transport coefficients. The kinetic equation is solved by the Chapman-Enskog method and the coefficients of shear viscosity, bulk viscosity, thermal conductivity, and self-diffusion are obtained. The predicted bulk viscosity and thermal conductivity coefficients are singular at the critical point, while the shear viscosity and self-diffusion coefficients are not.     

Bi-velocity transport processes. Single-component liquid and gaseous continua

The present contribution supplements the previous findings regarding the need for two independent velocities rather than one when quantifying mass, momentum and energy transport phenomena in fluid continua. Explicitly, for the case of single-component fluids the present paper furnishes detailed expressions for the phenomenological coefficients appearing in the constitutive equations governing these bi-velocity transport processes. Whereas prior analyses furnished coefficient values only for the case of dilute monatomic gases using data from Burnett’s solution of the Boltzmann equation, the present study furnishes values applicable to all fluids, liquids as well as dense gases. Moreover, whereas prior coefficient calculations derived these values (for dilute monatomic gases) from Burnett’s solution of Boltzmann’s gas-kinetic equation, the latter a molecular theory, the present analysis derives the liquid- and gas-phase values from purely macroscopic data requiring knowledge only of the fluid’s coefficients of thermal expansion, isothermal compressibility, and thermometric diffusivity. In the dilute monatomic gas case common to both levels of analysis, the respective molecularly and macroscopically derived phenomenological coefficients are found to be in excellent agreement, confirming the credibility of both bi-velocity theory and the theory establishing the values of the phenomenological coefficients appearing in the constitutive relations derived therefrom. Whereas the preceding macroscopic calculations invoked Onsager’s reciprocal theorem relating coupled phenomenological coefficients, an alternative scheme is presented at the conclusion of the paper, one that reverses the usual order of things, at least in the present single-component fluid case. This alternate scheme enables Onsager’s nonequilibrium reciprocal relation, originally derived by him using molecular arguments, to be derived using purely macroscopic arguments originating from knowledge of Maxwell’s equilibrium reciprocal relations, the latter fundamental to equilibrium thermodynamics.     

Enskog-Landau kinetic equation for multicomponent mixture. Analytical calculation of transport coefficients

The Enskog-Landau kinetic equation is considered to describe non-equilibrium processes of a mixture of charged hard spheres. This equation has been obtained in our previous papers by means of the non-equilibrium statistical operator method. The normal solution of this kinetic equation found in the first approximation using the standard Chapman-Enskog method is given. On the basis of the found solution the flows and transport coefficients have been calculated. All transport coefficients for multicomponent mixture of spherical Coulomb particles are presented analytically for the first time. Numerical calculations of thermal conductivity and thermal diffusion coefficient are performed for some specific mixtures of noble gases of high density. We compare the calculations with those ones for point-like neutral and charged particles. Received 10 June 1999 and Received in final form 15 October 1999     

Theory of surface excess Miesowicz viscosities of planar nematic liquid crystal-isotropic fluid interfaces

An expression for the surface excess stress tensor for planar compressible interfaces between rod-like nematic liquid crystals and isotropic viscous fluids is derived using the classical surface excess theory formalism, adapted to capture the intrinsic anisotropy of the nematic orientational ordering. A required step in the theory is to find the actual stress tensor in the three-dimensional interfacial region, which is obtained by a decomposition of the kinematic fields (rate of deformation tensor and director Jaumann derivative) into tangential, normal, and mixed components with respect to the interface. The viscosity coefficients appearing in the surface excess stress tensor are expressed in terms of interfacial and bulk viscosities for planar, constant orientation, flows. The expressions are used to define the three fundamental surface excess Miesowicz shear viscosities, in analogy with the three bulk Miesowicz shear viscosities. The ordering in the magnitudes of the surface excess Miesowicz shear viscosities is shown to depend on the magnitude of the surface scalar nematic order parameter relative to that of the adjoining bulk nematic phase. When the surface scalar order parameter is greater than in the bulk, the classical ordering in terms of magnitudes of the three bulk Miesowicz shear viscosities is recovered. On the other hand, when the surface scalar order parameter is smaller than in the bulk, the classical ordering in terms of magnitudes of the three viscosities does not hold, and inequality transitions are predicted as the surface scalar order parameter increases towards the bulk value. Received 5 July 1999 and Received in final form 16 November 1999     

Transport coefficients of liquid N2 computed by molecular dynamics

Summary With three potential functions including quadrupole interaction, we computed the shear and the bulk viscosity coefficients as well as the thermal conductivity by molecular dynamics for a number of states of liquid nitrogen. The results indicated that the transport coefficients are determinable with a statistical error of about 10 per cent, even for the angledependent molecular potentials in the rigid-rotor approximation. An exception represents the bulk viscosity, for which systems of large particle numbers are necessary to reach the few perent accuracy for states near the triple point. The quadrupole interaction affects weakly the time correlation functions and thus the transport coefficients. In several cases, it improves, however, the agreement with experimental data. Paper presented at the workshop ?Highlights on Simple Liquids?, held in Turin at ISI on 1–3 May, 1989.     

Flux expressions and NEMD perturbations for models of semi-flexible molecules

We derive energy and momentum flux expressions, for systems composed of a general class of semi-flexible molecules, in the Ciccotti-Ferrario-Ryckaert linear constraint formalism. According to this formalism, the whole set of Cartesian coordinates is divided into basic (independent) and secondary (dependent) subsets. It is found that energy and momentum flux vectors have a simple and general expression using both basic and secondary coordinates. In the case of non-equilibrium molecular dynamics, we give general and simple heat and shear flow algorithms, deriving the dissipative fluxes in the space of all Cartesian coordinates. In comparison with previous derivations for some models of flexible molecules, the present approach has more general applicability. Moreover, it leads to more efficient equilibrium and non-equilibrium molecular dynamics calculations of transport coefficients, and requires minimal programming effort.     

关联函数的长时间渐近行为——波对弛豫过程的影响

本文从非平衡态统计的一般理论出发,系统地讨论了宏观体系中波对弛豫过程的影响,特别是关联函数的非指数型渐近行为。由于表象选择对处理耗散过程的重要性,我们必须从元激发表象出发(而不是自由粒子表象)计算关联函数或输运系数(久保公式)。为此,应用了C代数的基本概念,发展了一套算子展开的方法,用之将流算子在元激发二次量子化表象中一般地表示出来。我们从刘维算子的预解式出发,对元激发间的剩余相互作用作微扰,应用了投影算子方法后,可以比较简单地得到关联函数非指数衰减部分的一般表达式。根据对元激发处理过程的分析,我们将元激 关键词：     

Dissipative squeezed vacuum in non-equilibrium thermo field dynamics

Degenerate parametric amplification accompanied by dissipation is analyzed within the canonical operator formalism for quantum dissipative systems named non-equilibrium thermo field dynamics. The vacuum of the system is subject to both dissipation and breaking of phase symmetry due to squeezing. The annihilation-creation operators for the vacuum are derived and the structure of the vacuum is examined. The effects of dissipation on squeezing and uncertainty relation are estimated.     

Generalized entropy and transport coefficients of hadronic matter

We use the generalized entropy four-current of the Müller-Israel-Stewart (MIS) theories of relativistic dissipative fluids to obtain information about fluctuations around equilibrium states. This allows one to compute the non-classical coefficients of the entropy 4-flux in terms of the equilibrium distribution functions. The Green-Kubo formulae are used to compute the standard transport coefficients from the fluctuations of entropy due to dissipative fluxes.     

On the theory of fluctuations around non-equilibrium steady states: A generalized time-convolutionless projector formalism

A new method of finding nonlinear Langevin type equations of motion for relevant macrovariables and the corresponding master equation for systems far from thermal equilibrium is presented by generalizing the time-convolutionless formalism proposed previously for equilibrium hamiltoian systems by Tokuyama and Mori. The Langevin type equation consists of a fluctuating force, and the nonlinear drift coefficients which are always identical to those of the master equation. A simple formula which relates the drift coefficients to the time correlation of the fluctuating forces is derived. This is a generalization of the fluctuation-dissipation theorem of the second kind in equilibrium systems and is valid not only for transport phenomena due to internal fluctuations but also for transport phenomena due to externally-driven fluctuations. A new cumulant expansion of the master equation is also obtained. The conditions under which a Langevin and a Fokker-Planck equation of a generalized type for non-equilibrium open systems can be derived are clarified.The theory is illustrated by studying hydrodynamic fluctuations near the Rayleigh-Bénard instability. The effects of two kinds of fluctuations, internal fluctuations of irrelevant macrovariables and external (thermal) noises, on the convective instability are investigated. A stochastic Ginzburg-Landau type equation for the order parameter and the corresponding nonlinear Fokker-Planck equation are derived.     

Note on the Kaplan–Yorke Dimension and Linear Transport Coefficients

A number of new relations between the Kaplan–Yorke dimension, phase space contraction, transport coefficients and the maximal Lyapunov exponents are given for dissipative thermostatted systems, subject to a small but non-zero external field in a nonequilibrium stationary state. A condition for the extensivity of phase space dimension reduction is given. A new expression for the linear transport coefficients in terms of the Kaplan–Yorke dimension is derived. Alternatively, the Kaplan–Yorke dimension for a dissipative macroscopic system can be expressed in terms of the linear transport coefficients of the system. The agreement with computer simulations for an atomic fluid at small shear rates is very good.     

Thermal cellular automata fluids

The concepts of local temperature and local thermal equilibrium are introduced in the context of lattice gas cellular automata (LGGAs) whose dynamics conserves energy. Green-Kubo expressions for thermal transport coefficients, in particular for the heat conductivity, are derived in a form, equivalent to those for continuous fluids. All thermal transport coefficients are evaluated in Boltzmann approximation as thermal averages of matrix elements of the inverse Boltzmann collision operator, fully analogous to the results for continuous systems, and fully model-independent. The collision operator is expressed in terms of transition probabilities between in- and out-states. Staggered diffusivities arising from spuriously conserved quantities in LGCAs are also calculated. Examples of models with either cubic or hexagonal symmetries are discussed, where particles may or may not have internal energies.     

Dissipative or just nonextensive hydrodynamics? — Nonextensive/dissipative correspondence

We argue that there is correspondence between the perfect nonextensive hydrodynamics and the usual dissipative hydrodynamics, which we call nonextensive/dissipative correspondence (NexDC). It leads to simple expression for dissipative entropy current and allows for predictions for the ratio of bulk and shear viscosities to entropy density, ζ/s and η/F.     

Phänomenologische Zustandsgrößen,Regressions-Schwankungs-Sätze und Transportkoeffizienten in linearen Onsager-Systemen

Starting from Onsager's assumption that the dynamical equilibrium correlations can be separated into a microscopic and a hydrodynamic part it is shown how to obtain phenomenological state variables in non-equilibrium, regression fluctuation theorems and (in some important cases) microscopic representations of thermal transport coefficients. The results are demonstrated for “pure” heat conduction, but most of them can be easily extended to systems which are described initially by the densities of dynamical constants.