A variational formulation of relativistic hydrodynamics

We combine Taub's and Ray's variational approaches to relativistic hydrodynamics of perfect fluids into another simple formulation.     

Suppression of elliptic flow in a minimally viscous quark–gluon plasma

We compute the time evolution of elliptic flow in non-central relativistic heavy-ion collisions, using a (2+1$2+1$)-dimensional code with longitudinal boost-invariance to simulate viscous fluid dynamics in the causal Israel–Stewart formulation. We show that even “minimal” shear viscosity η/s=?/(4π)$\eta /s=?/(4\pi )$ leads to a large reduction of elliptic flow compared to ideal fluid dynamics, raising questions about the interpretation of recent experimental data from the Relativistic Heavy Ion Collider.     

General relativistic Boltzmann equation, I: Covariant treatment

This series of two articles aims at dissipating the rather dense haze existing in the present literature around the General Relativistic Boltzmann equation. In this first article, the general relativistic one-particle distribution function in phase space is defined as an average of delta functions. Thereupon, the general relativistic Boltzmann equation, to be obeyed by this function, is derived. The use of either contravariant or covariant momenta leads to different, but equivalent, forms of the equation.The results of the present article are covariant, but not manifestly covariant. The transition to a manifestly covariant treatment, on the basis of off-shell momenta, is given in the second article.     

Anisotropic fluid dynamics in the early stage of relativistic heavy-ion collisions

A formalism for anisotropic fluid dynamics is proposed. It is designed to describe boost-invariant systems with anisotropic pressure. Such systems are expected to be produced at the early stages of relativistic heavy-ion collisions, when the timescales are too short to achieve equal thermalization of transverse and longitudinal degrees of freedom. The approach is based on the energy–momentum and entropy conservation laws, and may be regarded as a minimal extension of the boost-invariant standard relativistic hydrodynamics of the perfect fluid. We show how the formalism may be used to describe the isotropization of the system (the transition from the initial state with no longitudinal pressure to the final state with equal longitudinal and transverse pressure).     

General relativistic Boltzmann equation, II: Manifestly covariant treatment

In a preceding article we presented a general relativistic treatment of the derivation of the Boltzmann equation. The four-momenta occurring in this formalism were all on-shell four-momenta, verifying the mass-shell restriction p²=m²c². Due to this restriction, the resulting Boltzmann equation, although covariant, turned out to be not manifestly covariant. In the present article we switch from mass-shell momenta to off-shell momenta, and thereby arrive at a Boltzmann equation that is manifestly covariant.     

Viscosity and thermodynamic properties of QGP in relativistic heavy-ion collisions

We study the viscosity and thermodynamic properties of QGP at RHIC by employing the recently extracted equilibrium distribution functions from two hot QCD equations of state of O(g ⁵) and O(g ⁶ln (1/g)), respectively. After obtaining the temperature dependence of the energy density and the entropy density, we focus our attention on the determination of the shear viscosity for a rapidly expanding interacting plasma, as a function of temperature. We find that the interactions significantly decrease the shear viscosity. They decrease the viscosity to entropy density ratio, as well.     

Generalized Pearson distributions for charged particles interacting with an electric and/or a magnetic field

The linear Boltzmann equation for elastic and/or inelastic scattering is applied to derive the distribution function of a spatially homogeneous system of charged particles spreading in a host medium of two-level atoms and subjected to external electric and/or magnetic fields. We construct a Fokker-Planck approximation to the kinetic equations and derive the most general class of distributions for the given problem by discussing in detail some physically meaningful cases. The equivalence with the transport theory of electrons in a phonon background is also discussed.     

Nonextensive effects on the phase structure of quantum hadrodynamics

In this Letter, we investigate nonextensive effects on phase transition in nuclear matter in the context Walecka many-body field theory. A difference is observed when the results calculated for the nuclear matter at vanishing baryon density is compared to those obtained through the standard Fermi-Dirac distribution. It is observed a dependence between the nonextensive parameter q and the coupling constants of the phase transition. A numerical relation for this thermodynamical dependence is also proposed.     

On the dynamics of exotic matter: Towards creation of Perpetuum Mobile of third kind

The one-dimensional dynamics of a classical ideal ‘exotic’ fluid with equation of state p=p(?)<0$p=p(\mathrm{?})<0$ violating the weak energy condition is discussed. Under certain assumptions it is shown that the well-known Hwa–Bjorken exact solution of one-dimensional relativistic hydrodynamics is confined within the future/past light cone. It is also demonstrated that the total energy of such a solution is equal to zero and that there are regions within the light cone with negative (−)$(-)$ and positive (+)$(+)$ total energies. For certain equations of state there is a continuous energy transfer from the (−)$(-)$-regions to the (+)$(+)$-regions resulting in indefinite growth of energy in the (+)$(+)$-regions with time, which may be interpreted as action of a specific ‘Perpetuum Mobile’ (Perpetuum Motion). It is speculated that if it is possible to construct a three-dimensional non-stationary flow of an exotic fluid having a finite negative value of energy such a situation would also occur. Such a flow may continuously transfer positive energy to gravitational waves, resulting in a runaway. It is conjectured that theories plagued by such solutions should be discarded as inherently unstable.     

Early evolution of transversally thermalized partons

The idea that the parton system created in relativistic heavy-ion collisions (i) emerges in a state with transverse momenta close to thermodynamic equilibrium and (ii) its evolution at early times is dominated by the 2-dimensional (transverse) hydrodynamics of the ideal fluid is investigated. It is argued that this mechanism may help to solve the problem of early equilibration.     

Properties of baryonic,electric and strangeness chemical potentials and some of their consequences in relativistic heavy ion collisions

Analytic expressions are given for the baryonic, electric and strangeness chemical potentials which explicitly show the importance of various terms. Simple scaling relations connecting these chemical potentials are found. Applications to particle ratios and to fluctuations and related thermal properties such as the isothermal compressibility κT${\kappa }_T$ are illustrated. A possible divergence of κT${\kappa }_T$ is discussed.     

The property of κ-deformed statistics for a relativistic gas in an electromagnetic field: κ parameter and κ-distribution

We investigate the physical property of the κ parameter and the κ-distribution in the κ-deformed statistics, based on Kaniadakis entropy, for a relativistic gas in an electromagnetic field. We derive two relations for the relativistic gas in the framework of κ-deformed statistics, which describe the physical situation represented by the relativistic κ-distribution function, provide a reasonable connection between the parameter κ  , the temperature four-gradient and the four-vector potential gradient, and thus present for the case κ≠0$\kappa \ne 0$ one clearly physical meaning. It is shown that such a physical situation is a meta-equilibrium state of the system, but has a new physical characteristic.     

Giant switch-on and switch-off currents in device “electrode-molecule-electrode”

The transient current formation in a device “electrode-single molecule-electrode” is studied theoretically. It is demonstrated that a giant transient current is formed if the two transfer couplings of the molecule to the electrodes differ strongly and if the applied voltage is instantaneously switched on or off. This behavior is mainly caused by a recharge of the molecule due to nonequilibrium electron hopping processes from or into the electrodes.     

Formation and decay of hadronic resonances in the QGP

Hadronic resonances can play a pivotal role in providing experimental evidence for partial chiral symmetry restoration in the deconfined quark–gluon phase produced at RHIC and the LHC. Their lifetimes, which are comparable to the lifetime of the partonic plasma phase, make them an invaluable tool to study medium modifications to the resonant state due to the chiral transition. In this Letter we show that the heavier, but still abundant, light and strange quark resonances K^∗$K^{\ast }$, ?, Δ   and Λ^∗${\Lambda }^{\ast }$ have large probability to be produced well within the plasma phase due to their short formation times. We demonstrate that, under particular kinematic conditions, these resonances can be formed and will decay inside the partonic state, but still carry sufficient momentum to not interact strongly with the hadronic medium after the QCD phase transition. Thus, K^∗$K^{\ast }$, ?, Δ   and Λ^∗${\Lambda }^{\ast }$ should exhibit the characteristic property modifications which can be attributed to chiral symmetry restoration, such as mass shifts, width broadening or branching ratio modifications.     

Dynamic subgrid scale modeling of turbulent flows using lattice-Boltzmann method

In this paper, we discuss the incorporation of dynamic subgrid scale (SGS) models in the lattice-Boltzmann method (LBM) for large-eddy simulation (LES) of turbulent flows. The use of a dynamic procedure, which involves sampling or test-filtering of super-grid turbulence dynamics and subsequent use of scale-invariance for two levels, circumvents the need for empiricism in determining the magnitude of the model coefficient of the SGS models. We employ the multiple relaxation times (MRT) formulation of LBM with a forcing term, which has improved physical fidelity and numerical stability achieved by proper separation of relaxation time scales of hydrodynamic and non-hydrodynamic modes, for simulation of the grid-filtered dynamics of large-eddies. The dynamic procedure is illustrated for use with the common Smagorinsky eddy-viscosity SGS model, and incorporated in the LBM kinetic approach through effective relaxation time scales. The strain rate tensor in the SGS model is locally computed by means of non-equilibrium moments of the MRT-LBM. We also discuss proper sampling techniques or test-filters that facilitate implementation of dynamic models in the LBM. For accommodating variable resolutions, we employ conservative, locally refined grids in this framework. As examples, we consider the canonical anisotropic and inhomogeneous turbulent flow problem, i.e. fully-developed turbulent channel flow at two different shear Reynolds numbers Re_∗ of 180 and 395. The approach is able to automatically and self-consistently compute the values of the Smagorinsky coefficient, C_S. In particular, the computed value in the outer or bulk flow region, where turbulence is generally more isotropic, is about 0.155 (or the model coefficient ) which is in good agreement with prior data. It is also shown that the model coefficient becomes smaller and approaches towards zero near walls, reflecting the dampening of turbulent length scales near walls. The computed turbulence statistics at these Reynolds numbers are also in good agreement with prior data. The paper also discusses a procedure for incorporation of more general scale-similarity based SGS stress models.     

The non-equilibrium work relation: Thermodynamic analysis and microscopic foundations

We discuss the conditions for which the non-equilibrium work relation is valid by means of thermodynamic and microscopic arguments.